R 语言学习课程内容提交

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---
title: |
| DataWhale 组队学习 R语言数据分析
| Task 0 入门篇
author: "Fin"
date: "`r Sys.Date()`"
header-includes:
- \usepackage{ctex}
urlcolor: blue
output:
prettydoc::html_pretty:
theme: cayman
highlight: github
number_section: yes
toc: no
knit: (function(inputFile, encoding) {
rmarkdown::render(inputFile, encoding = encoding,
output_dir = "output", output_format = "all") })
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,warning=FALSE, message=FALSE,tidy=TRUE,collapse=FALSE)
```
![](./image/task00_intro_structure.jpg){width=100%}
# 安装
## R
* R语言是一门用于统计计算与绘图的编程语言和开源软件([The R Foundation](https://www.r-project.org/))。
* R语言是当今应用最多的统计软件之一。
* 截止到这份文档编写时在CRAN ([the Comprehensive R Archive Network](https://cran.r-project.org/))上总共发行了`r format(ifelse((nn <- nrow(available.packages(contrib.url("https://cran.rstudio.com/", "both")))) < 17619, 17619, nn), scientisfic = FALSE)`个R语言程辑包。
* 除了CRAN以外R语言的程辑包作者也在其他线上代码托管与研发协作平台发布了数不尽的作品。这样的平台包括[GitHub](https://github.com/)、[GitLab](https://about.gitlab.com)、[Gitee](https://gitee.com/)等。
你可以从CRAN的网站上下载Rhttps://cloud.r-project.org/。
你也可以在[这里](https://cran.r-project.org/mirrors.html)选择任意一个镜像网站来下载R.
## RStudio
[RStudio](https://rstudio.com/products/rstudio/)是针对R语言设计的集成开发环境。如果没有RStudio的话R本身只提供一个简单的文本编辑器。如果把R语言本身比喻成飞机的话那么RStudio便是飞机场你不需要它就可以飞但是有了它会极大增加效率。它包括一个控制台、语法突出显示的编辑器、直接执行代码的支持以及用于绘图、历史记录、调试和工作区管理的工具。
你可以从其官网下载开源版本https://rstudio.com/products/rstudio/
在本文档中我们会介绍RStudio的用户界面和部分功能帮助你尽快上手使用RStudio的数据分析。
## R语言程辑包R Package
R语言程辑包是R语言必不可少的部分。R语言能有他今天在统计学里的位置正是归功于其程辑包在统计计算方面的发展。一个程辑包为用户提供函数function、数据data或者插件addins。除了R本身自带的基础程辑包base、utils、stats等以外你还可以用以下代码来从CRAN上下载并安装额外的程辑包
```{r, eval = FALSE}
install.packages("tidyverse")
```
我们将会在这次组队学习中多次用到`tidyverse`。它其实是一系列程辑包的组合,主要提供数据清洗与处理的工具。
### 进阶的安装方法
当你应用R语言的能力到一定阶段之后你会发现自己需要安装不在CRAN上发布的程辑包或者你需要最新版本的程辑包CRAN上的包为了保证代码的可靠性发布前需要经过一系列的检查与测试这就导致CRAN上的版本往往不是最新的开发版本。以安装GitHub上发布的程辑包为例你可以使用以下代码
```{r, eval = FALSE}
# 安装remotes包
install.packages("remotes")
# 使用remotes从GitHub上安装username名下的repo包
remotes::install_github("username/repo")
```
我们需要先安装`remotes`包,并使用其中的`install_github`函数来完成操作。注意这里是从源代码安装在本地编译。Windows用户需要使用Rtools作为背后的编译工具。关于Rtools的安装信息见 https://cran.r-project.org/bin/windows/Rtools/
### R与其程辑包的更新
在本文档编写之时R语言已更新到版本`r R.version$version.string`。当新的版本发布时,你可以使用`installr`包中的`installr`函数来完成R的更新你当然也可以手动下载更新如果不嫌麻烦的话。代码如下
```{r, eval = FALSE}
# 安装installr包
install.packages(installr)
# 更新R
installr::installr()
```
根据对话窗口中的提示完成整个安装过程即可。
你也可以使用以下代码来更新R的程辑包
```{r, eval = FALSE}
# 手动确认是否将各个更新到最新版本,或者
update.packages()
# 更新所有包到最新版本
update.packages(ask = FALSE)
```
# 环境配置
## 项目Project
在RStudio中一个项目Project本质上是一个把项目相关的文件储存在一个地方的文件夹。如果使用项目相关的功能的话你不需要担心使用的文件是否在当前的工作目录Working Directory。 项目功能提供了一个将不同目的的文件分隔开的方式,同时自动保存上次相应的工作进度。
### 练习 {-}
为这次组队学习建立一个新的项目。
每次进行组队学习的时候不要忘记去打开这个项目。在结束工作退出R或者切换到另一个项目的时候为了下次打开RStudio的时候有一个干净的工作环境建议不去保存“工作空间镜像” Workspace image即在当前进程中加载的数据、函数
创建新的项目,可以在下拉菜单 __File__ 或者RStudio界面的右上角找到 __New Project__ 选项。在弹出的对话框中,如果你想创建一个新的文件夹作为项目文件夹,选择 __New Directory__ ;如果你想用一个已经存在的文件夹作为项目文件夹,选择 __Existing Directory__ 。
![RStudio界面右上角的项目设置^[小提示如果想要改变RStudio的主题颜色可以通过 __Tools__ >> __Global Options..__ >> __Appearance__]](./image/task00_project.png)
## 用户界面
接下来让我们关注一下RStudio用户界面里的各种面板和标签。在这一部分有四个基础面板值得注意。
* __Console__ 控制台位于界面左侧。你可以在这里运行命令、浏览输出结果。
* __Environment__ 位于界面右上方。环境面板会总结出当前加载的数据、定义的函数等。现在在你看来可能是空的,因为我们还没有做任何事情。
* __Files__ 位于界面右下方。文件面板展示当前文件夹的信息。
* __Help__ 帮助面板也位于界面右下方。在这里你可以找到相应数据或者函数的帮助信息。
## R Markdown
你可以控制台Concole直接运行命令但是这样跑出来的指令不会被保存下来。一般来说我们更建议将命令写在叫做R script的脚本中或者写在一个叫做R Markdown的文件中。
### 练习 {-}
创建一个脚本 R script.
* __File__ >> __New File__ >> __R Script__
### 练习 {-}
创建一个R Markdown文件。
* __File__ >> __New File__ >> __R Markdown..__
在脚本或者R Markdown的界面中界面上方可以找到一个运行所有代码的按键。
一个R Markdown文件是一个可以将代码与 _markdown_ 标准文本一种纯文本的格式语法结合在一起的文本文档。使用R Markdown文件可以很容易地生成pdf文件或者html文件其中不止包含了你的文本还有代码以及运行代码所生成的结果。点击界面上方的 __Knit__ 按键^[如果你想要生成pdf文件你需要安装[LaTeX](https://www.latex-project.org/)。可以看看很好地兼容了R的[TinyTex](https://yihui.org/tinytex/)。]即可。再也不需要复制粘贴、屏幕截图输出结果到Wrod了。R Markdown文档的一个主要优势是可复现。只要有了同样的代码和数据你可以获得与其他人一模一样的结果只要生成文档就可以了。
在R Markdown文件里写代码需要使用特定的代码块code chunks来告诉R Markdown这部分是需要运行的代码而不只是文本。^[R Markdown的更多语法可以看看 [R Markdown cheatsheet](https://rstudio.com/wp-content/uploads/2016/03/rmarkdown-cheatsheet-2.0.pdf)。]
````markdown
`r ''````{r}
# 在这里写你的代码
# 使用三个反引号和 {r} 起始,三个反引号结束来构建代码块
# 在代码块里使用井号 # 写评论(纯文本)
`r ''````
````
## 帮助
R能够发展到其今天的地位很大的一个因素是他提供了相对详细的帮助文档对初学者相对友好。一个相对完整的R包最低标准便是有函数的帮助文档。需要查看一个具体函数或者数据的帮助时可以用`?fun`(等同于`help(fun)`),该函数`fun`的帮助文档便会出现在之前提到过的帮助面板里。这个是已经知道需要什么函数了之后查找具体函数的用法的方式,如果你不记得具体的函数名字,可以使用两个问号加关键字来搜索:`??keyword`。
其次R包会有一个或多个vignette。vignette文档的目的主要是当使用者不知道用什么函数对这个包不了解的时候提供一份入门简介一样的东西一般会对常用的函数做出说明和演示以及一些理论的阐述。这个包如果是哪一篇论文的副产品vignette甚至有可能是这篇论文。根据包的大小不同vignette的数量也不一样。如果是针对于一个问题写出的精炼的小包的话会只有一个vignette。如果包的用途比较广泛或者作者想说的话比较多会针对每个问题有一个单独的vignette。浏览所有已安装的vignette用`browseVignettes()`,查看具体包的用`browseVignettes("packagename")`。以上两个是通过CRAN发行的包的标配。
如果这个包没有在CRAN上发行只在GitHub上或者GitHub上有开发版本的话一般会有一个`README.md`的文档。这个文档相对于vignette来说更加简短一般都只写明如何安装以及最主要的命令的演示没有太多的说明。文档最后有可能会说明这个包用的是什么许可证。如果有这么一个文件的话就可以很快速的知道这个包最主要的命令是什么。这个文档就需要到相对应的R包的资源库搜索了。
```{r, eval = FALSE}
## 总结
# 查看具体函数的帮助文档
?fun
help(fun)
# 在帮助文档中搜索关键词
??keyword
# 浏览所有已安装的vignette
browseVignettes()
# 查看具体包的vignette
browseVignettes("packagename")
```
# Happy Coding!
这次的R语言数据分析组队学习的入门篇便到这里了。接下里请移步组队学习的正篇第一部分数据结构与数据集。
玩得开心!
----
By: Fin
> https://yangzhuoranyang.com
关于Datawhale Datawhale是一个专注于数据科学与AI领域的开源组织汇集了众多领域院校和知名企业的优秀学习者聚合了一群有开源精神和探索精神的团队成员。Datawhale 以“for the learner和学习者一起成长”为愿景鼓励真实地展现自我、开放包容、互信互助、敢于试错和勇于担当。同时 Datawhale 用开源的理念去探索开源内容、开源学习和开源方案,赋能人才培养,助力人才成长,建立起人与人,人与知识,人与企业和人与未来的联结。 本次数据挖掘路径学习专题知识将在天池分享详情可关注Datawhale
[![logo.png](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)

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---
title: |
| DataWhale 组队学习 R语言数据分析
| Task 1 数据结构与数据集篇
author: "Fin"
date: "`r Sys.Date()`"
header-includes:
- \usepackage{ctex}
urlcolor: blue
output:
prettydoc::html_pretty:
theme: cayman
highlight: github
number_section: yes
toc: no
knit: (function(inputFile, encoding) {
rmarkdown::render(inputFile, encoding = encoding,
output_dir = "output", output_format = "all") })
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, cache = TRUE,warning=FALSE, message=FALSE,tidy=TRUE,collapse=FALSE)
```
![](./image/task01_data_structure.jpg){width=100%}
# 准备工作
这节组队学习的目的主要是帮助你上手R的基本编程逻辑了解一些R编程的基本概念包括各个数据类型和数据集的读取与保存。
在开始我们的学习之前不要忘记在R Studio中切换到组队学习专属的项目打开一个R script 文件或者R Markdown文件详见入门篇
# 编码基础
首先我们来了解一些基本的编码操作。在R Studio中想要运行代码可以在控制台Console中键入代码后点击回车。这样运行的代码会被保存在当前项目的`.Rhistory`文件中也可以在R Studio 界面右上角的 History 面板中找到但是不会被明确地保存下来作为一个脚本文件。一般只有在我们想要运行一些简单的指令或者计算的时候才会采取这种方式。更常见的是将代码写在脚本文件中选中相应的代码后点击界面上方的Run或者快捷键`Ctrl` + `Enter`)来运行。
## 算术
你可以直接运行计算命令。计算符号包括加`+`、减`-`、乘`*`、除`/`、求幂`^`以及求余数`%%`等。值得一提的是开平方根有他自己单独的函数`sqrt`。
```{r}
1 + 1
1 - 1
1 * 2
1 / 2
3 %% 2
2^(1 / 2)
sqrt(2)
```
## 赋值
在R里我们可以为一个“东西”取一个名字这个“东西”可以是一个值、一个向量、或者一个函数等这样我们就可以之后再获取存储在这个名字下面的信息。
```{r}
# 将数字42赋予名叫x的变量
x <- 42
# 在R中运行一个物体的名字
# R将会打印出print该物体的值
x
```
在R中基础赋值的符号有三种
1. 一个向左的箭头`<-`表示将箭头右方的值取名叫做箭头左侧的名字,或者将箭头右侧的值存储在箭头左侧的名字里;
2. 一个向右的箭头`->`表示将箭头左侧的值储存在箭头右侧的名字里;
3. 一个等号`=`表示将箭头右侧的值存储在箭头左侧的名字里同1
在早期的键盘中有一个单独的按键就是向左的箭头虽然后来的键盘不再设立这个按键但是使用箭头的编程习惯流传了下来。赋值符号的选择取决于个人习惯但是我们大多数情况下都推荐使用箭头尤其是向左的箭头作为赋值的符号。这是R语言于其他语言不同的地方有以下原因
1. 箭头明确了赋值方向,这是等号做不到的;
2. 等号用在顶层环境中的时候是赋值,用在函数中则是设参(或者叫做在函数层面赋值)。这种二义性不小心区分则可能会引发错误。而等号即使用在函数中也是赋值;
3. 箭头可以做到多次赋值(`a <- b <- 42`)甚至是不同方向上多次赋值(`a <- 42 -> b`)(尽量避免!);
4. 虽然这次组队学习中不会学到,但是更高级的赋值工具包括 `<<-` 和 `->>` 对应向左或向右的箭头;
5. 同时使用`=`与`==`(判断是否相等)会降低可读性(`a <- 1 == 2` vs `a = 1 == 2`)。
总结__凡是赋值都用`<-`__凡是设参之后会说到都用`=`。
在R Studio中可以使用快捷键`Alt` + `-`来输入`<-`这样就不用每次都点两次键啦。这样还有一个好处就是R Studio会自动识别当前的输入语言从而选择最佳的赋值符号。大多数情况下这也就是说他会输入R的`<-`如果你在R Studio里用Python的话就会自动变成`=`啦。
原来作用于单纯数字上的算术运算现在即可用变量名称代替具体的数值。
```{r}
y <- 21
x + y
x <- x + y
```
## 函数
R是一个非纯函数式编程Functional Programming的语言与你平时可能所熟悉的面向对象程序设计Object-Oriented Programming的编程语言比如Python不一样。这意味着在R中相对于以类Class与对象Object的思路思考问题我们要更多地定义函数Function以及考虑函数的输入与输出来进行运算。如果你不知道我在这里说什么请忽略这段话。
在R中所有的运算都是通过函数来达成的。我们可以用和之前一样的赋值方法`<-`)来将一个函数存储在一个名字下。请看以下示例:
```{r}
addone <- function(x = 0) {
x + 1
}
```
这里我创建了一个名为`addone`的函数,这个函数的作用就是将输入值在函数内部存储在名为`x`的参数里,在名为`x`的值上加一,再返回结果。如果没有输入值的话,`x`的默认值是`x = 0`。
```{r}
# 作用在数字上
addone(42)
# 作用在变量上
y <- 42
addone(y)
```
如你可见调用函数的方法就是在函数的名字后边加小括号再在小括号中输入参数arguments。当函数有多个可选参数的时候建议输入参数的时候使用等号`=`明确函数名称。这便是之前提到过的等号的设参用法。
```{r}
addone(x = 42)
```
如果你没有使用小括号而是直接在控制台中运行函数的名字的话像以前一样R会直接打印出这个函数的内容即源代码
```{r}
addone
```
当你完成了一个复杂的计算,不要忘记把结果储存在一个名字下,否则结果不会保存下来,只会在控制台中一闪而过。
```{r}
y <- 42
y_plusone <- addone(y)
```
## 循环loop
使用代码很重要的一个原因是可以重复进行多次相同或有规律的操作,也就是循环了。
R中的循环函数包括`for``while`,和`repeat`。在这里我们简单用一个例子来介绍一下最灵活的`for`循环:
```{r}
x <- 0
for(i in 1:3){
x <- x + i
print(x)
}
```
在最开始的时候,我们让`x`等于0。在接下来进行的循环操作中紧跟在`for`之后的小括号里给出了每个回合当中会变化的参数,叫做`i`。`i`后边的`in`之后给出的是参数`i`在回合中的可能取值也就是从1到3的正整数。最后大括号中给出每个回合的操作在`x`上加上`i`的值,重新取名为`x`,再打印出来。
整个流程下来:
第一个回合`x`一开始是0在第一个回合中`i`是1经过计算赋值`x`变成了1打印后进入第二个回合
第二个回合`x`一开始是1在第二个回合中`i`是2经过计算赋值`x`变成了3打印后进入第二个回合
第三个回合`x`一开始是3在第三个回合中`i`是3经过计算赋值`x`变成了6打印后结束循环。
## 管道pipe
如果我们想要对一个对象进行多个函数的操作,比如说想要使用我们刚刚定义的`addone`函数,还有新定义的`addtwo``addthree`,我们可以按照普通调用函数的方法一个套一个:
```{r}
addone <- function(x) x+1
addtwo <- function(x) x+2
addthree <- function(x) x+3
x <- 0
addthree(addtwo(addone(x)))
```
在这种常规的方法下,函数运行的顺序,和我们读函数的顺序,都是从内到外的。比如在上边的操作中,我们先用了`addone`给0加1又用了`addtwo`,最后用了`addthree`。这样的坏处也是显而易见的,即可读性很差。想象一下你要对一个数据列表连续使用十几个函数,每个函数里都有其自己不同的参数,这么一系列操作如果用这个常规方法的话必然会使代码变成一个很难读的庞然大物。
`magrittr`包提供了另一种使用函数的办法,即使用`%>%`这个符号函数进行方法链method chain的操作。你可以把这个符号叫做管道。如果我们用管道来重写之前的一连串操作代码会变成
```{r}
# tidyverse也包含了管道符号
library(tidyverse)
x %>%
addone() %>%
addtwo() %>%
addthree()
```
这个符号的具体含义简单来说是“将上一步运行的结果放在下一步运行的函数的第一个参数的位置上”。在这个例子中,`x`被当作`addone`的第一个参数被加一。`addone`的运行结果被当成下一步`addtwo`的第一个参数被加二,其运行结果最后被当成`addthree`的第一个参数被加三,最终得到结果。
经过了管道的改写之后函数的可读性得到了大幅上升。从常规的“从内到外”读法变成了“从上到下从左到右”。虽然需要运行额外R包但是由于符合阅读习惯和数据清洗流程的特点管道在数据分析的领域被普遍使用。
关于管道符号的具体使用规则详见`` ?`%>%` ``。
# 数据类型
## 基础数据类型
在R中有五种基础数据类型包括三个数值型、一个逻辑型和一个字符型。
### 数值型
数值型数据包括三种分别是默认的实数数值型数据double、整数类型integer和复数类型complex
```{r}
# numeric
a <- 132.2345
# Inf
# integer
b <- 132L
# complex
c <- 2 + 3i
```
实数数值型数据每个值占用8个字节bytes是最常见的数值型数据。如果没有做特别处理我们平时见到的数字都是这个类型的——单纯的数字罢了。
整数类型正如它的名字一样只包含整数而没有小数部分。我们可以在整数末尾加上一个大写的L来表示这个数字是一个整数类型的数据。如果没有加大写的L的话虽然只输入了一个整数但是这个整数是实数数值类型的整数而不是整数类型。他们的区别在于实数数值类型的整数和和非整数一样都占用8个字节而整数类型只占用4个字节。平时用起来区别不大但是如果数据量比较大且都是整数的话推荐使用整数类型来节约空间。
复数类型便是包含复数部分的数值类型了。只要在实数部分后边加上虚数部分并且用小写字母i来代表虚数单位这个数值便是复数类型。鉴于数据分析领域基本不会涉及复数我们在这次组队学习不去讨论复数类型。
判断一个数值是什么类型,可以用`typeof()`:
```{r}
typeof(a)
typeof(b)
typeof(c)
```
### 逻辑型
逻辑型logical数据只包括两个值`TRUE``T` 和 `FALSE``F`:
```{r}
TRUE
T
FALSE
F
```
尽管一个字母的缩写和全拼效果是一样的,但是一个好的编程习惯是始终使用大写全拼的`TRUE`和`FALSE`。这样可以增加可读性,也会减小因为命名产生的使用错误。比如,有些时候涉及到时间序列时,一些用户喜欢将最大时序上限命名为`T`,这个时候就不能用`T`来代表`TRUE`了。
说到逻辑型数据就不得不说到逻辑算符。这里我们只考虑三个分别是“和”and`&`、“或”or`|`、“否”not`!`。
```{r}
TRUE & FALSE
TRUE | FALSE
!TRUE
```
### 字符型
字符型数据character可以总结为“任何带引号的值”。它可以是一个字母、一个单词、一句话、或者任何用引号框起来的数值或逻辑。
```{r}
string_a <- "A"
string_b <- "letter"
string_c <- "This is a sentence."
string_d <- "42"
string_e <- "TRUE"
```
在输入的时候,即使是数字或者逻辑型的`TRUE`和`FALSE`,只要加上了引号,他们就变成了字符型的数据,而不再带有数值型或逻辑型的特性。要注意区分。
```{r}
typeof(42)
typeof("42")
typeof(TRUE)
typeof("TRUE")
```
字符型是最“自由”的数据类型因为它的内容可以是任何字符任何其他的数据类型也可以转化为字符型数据。比如你可以把一个数值型数据加上引号来当作字符型数据来解读。但是反过来却不可以你没有办法把一个字符当作数字来解读。数据之间的转化我们会在第3.2.2节讲到。
在R中单引号`'`)和双引号(`"`)是等效的,但是我们推荐大多数情况下使用双引号,只有在引号内有双引号的时候使用单引号去引双引号(比如`' This is an "example". '`。这主要是为了帮助其他语言C, C++, Java等的用户区分单双引号的细微区别。在C语言里单双引号不是等效的。R语言中的双引号大致是与C语言中的双引号等效的。
## 向量vector
这里说到的向量主要指基础向量类型atomic vector
向量是由一组相同类型的值组成的一维序列。根据值的类型不同,我们会有不同类型的向量。
相对应之前的数值、逻辑和字符型的基础数据类型,这里我们也有数值、逻辑和字符型的向量类型。
```{r}
vec_num <- c(1, 2, 3)
vec_log <- c(TRUE, FALSE, TRUE)
vec_cha <- c("A", "B", "middle school")
```
使用函数`c()`来构建向量。可以进行向量上的运算,而不用一个一个值地单独去计算。
```{r}
vec_A <- c(1, 2, 3)
vec_B <- c(3, 5, 6)
vec_A + vec_B # 等同于 c(1 + 3, 2 + 5, 3 + 6)
!vec_log
```
也有相应的作用于向量上的函数,可以计算相应的统计量。比如求和的`sum`、求方差的`var`、平均值的`mean`等:
```{r}
sum(vec_A)
var(vec_A)
mean(vec_A)
```
### 因子factor
除了之前提到的基础数据类型组成的向量外,还有一类重要的的向量类型便是因子,可以使用函数`factor`和`c`组合来创建。
```{r}
vec_fac <- factor(c("male", "female", "male", "female", "female"))
vec_fac
```
从表面上看一个因子向量和字符向量很相似都是一系列带引号的字符组成的。它与字符向量的主要区别在于因子向量的独特值levels是有限个数的。因子向量的所有元素都是由这些有限个数的独特值组成的。比如在以上的例子中虽然`vec_fac`由五个元素组成但是只包括了两个独特值“male”和“female”。
```{r}
# 查看因子向量的独特值
levels(vec_fac)
```
你也可以用函数`ordered`或者`factor`里的`ordered = TRUE`参数argument创造一个有内在顺序的因子向量内在顺序可以用`levels`参数来手动设定:
```{r}
educ <- ordered(
c("kindergarten", "primary school", "middle school",
"primary school", "middle school", "kindergarten"),
levels = c("kindergarten", "primary school", "middle school")
)
# 等同于
educ <- factor(
c("kindergarten", "primary school", "middle school",
"primary school", "middle school", "kindergarten"),
ordered = TRUE,
levels = c("kindergarten", "primary school", "middle school")
)
educ
```
实质上R把因子向量当作整数型数值向量来对待。这也就意味着用因子向量替代字符向量可以剩下很多字节。
### 数值之间的转换 {#transform}
不同的向量/数据类型之间是可以互相转换的。相互转换的可行性取决于数据类型的复杂程度(或者说自由程度)。按照自由程度将已经提到的几种向量以从高到低的排序可得
> 字符>数值>逻辑
在数值型内的排序从自由度高到低为
> 复数>实数>整数
越靠近字符的类型越“自由”,自由度低的类型可以(随意)转化为同层或自由度更高的类型。字符型向量是最自由的:它可以包含任何原始值,其他任何类型都可以转化为它。我们以一个最受限制的逻辑向量为例,在这里展示如何根据这个排序使用几个常见的类型转换函数:
```{r}
vec_loc <- c(TRUE, FALSE, TRUE)
# 从逻辑型到数值型
vec_num <- as.numeric(vec_loc)
vec_num
# 从数值型到字符型
vec_cha <- as.character(vec_num)
vec_cha
# 从逻辑型到字符型
vec_cha2 <- as.character(vec_loc)
vec_cha2
## 倒序
# 从字符型到数值型
as.numeric(vec_cha)
# 从字符型到逻辑型
as.logical(vec_cha2)
# 从数值型到逻辑型
as.logical(vec_num)
```
这里我们可以看到逻辑型的`TRUE`和`FALSE`实际上对应数值型的1和0。
从一个低自由的类型可以随便转化到高自由的类型,但是反过来,从一个高自由的类型要转化到一个低自由的类型必须要符合一些特定值。比如:
1. 从字符型转化到数值型的时候,字符的值一定要符合数字的格式;
2. 从数值型转化到逻辑型0会转化为`FALSE`,其他数值会转化为`TRUE`
3. 从字符型转化到逻辑型,字符的值只能是`TRUE`和`FALSE`。
如果不符合这个规则的话,会得到`NA`。`NA`是“Not Available”的缩写即所谓的缺失值。缺失值的处理在下一篇《数据清洗与准备》会讲到。
```{r}
# 产生缺失值
as.logical(c("some", "random", "strings"))
```
因子型是一个相对特殊的类型,它可以和数值型与字符型相互转换。
```{r}
vec_fac <- factor(c("male", "female", "male", "female", "female"))
# 从因子型到数值型
vec_num <- as.numeric(vec_fac)
vec_num
# 从因子型到字符型
vec_cha <- as.character(vec_fac)
vec_cha
# 从字符型到因子型
as.factor(vec_cha)
# 从整数型到字符型
as.factor(vec_num)
```
正如之前所说R内部将因子变量当作整数变量来处理这也就是为什么一个看上去像是字符的东西可以被变成数值。
需要注意的是,把因子型转化为其他类型的时候会丢失一定的信息:
1. 因子向量变成字符向量会丢失独特值的信息;
2. 因子向量变成数值型的时候会丢失字面信息,只会保留独特值的编码,即根据独特值排序的正整数。
### 向量命名
除了向量自己的名字,我们也可以给向量里的每个元素一个名字。
```{r}
# 先命名向量
# 再命名向量的元素
vec <- c(1, 2, 3)
names(vec) <- c("A", "B", "C")
vec
# 或者
# 创造向量的时候命名向量的元素
vec <- c(A = 1, B = 2, C = 3)
vec
```
### 访问向量的子集
三种截取子集的符号:`[`、`[[` 和 `$`(其中`$`不能用在基础向量上)。
六种截取向量子集的方法:
1. 正整数:根据元素的序号提取元素;
2. 负整数:根据元素的序号去除元素;
3. 和向量长度一样的逻辑向量:将逻辑向量的元素与向量元素一一对应,`TRUE` 选择该元素,`FALSE`去除该元素;
4. Nothing选择原向量
5. 零0什么都不选择
5. 字符向量:选择根据元素名字选择元素。
使用`[` 作为选取符号的示例:
```{r}
vec <- c(a = 1.2, b = 5.6, c = 8.4, d = 9.5)
# 1. 正整数
vec[c(1,3)]
# 2. 负整数
vec[c(-1,-3)]
# 3. 逻辑向量
vec[c(TRUE, FALSE, FALSE, TRUE)]
# 4. Nothing
vec[]
# 5. 零
vec[0]
# 6. 字符向量
vec[c("a", "c")]
```
`[[` 在向量的场景里只能选择一个元素,而不是像`[` 一样选择一个子集:
```{r, error = TRUE}
# 可以
vec[[1]]
vec[1]
vec[c(1, 3)]
# 不可以
vec[[c(1, 3)]]
```
正是因为这个原因,我们提倡在只选择一个元素的时候多使用`[[`而不是`[`。这样在函数产生预期外的行为,选择多余一个元素的时候可以及时被错误信息提醒。
## 特殊数据类型
### 日期date
R中有蕴含日期的特殊类型`Date`,有日期-时间类型的`POSIXct`和`POSIXlt`。但在这一节我主要想介绍一下专注于日期处理的包`lubridate`。
```{r}
library(lubridate)
```
日期的本质实质上只是数字罢了但是日期也有特殊的计算方式特殊的进制。比如一个月有可能有30天或31一天多少天进一个月也需要相应变化。`lubridate`包中的年月日`ymd`函数就是用来帮助解决这个问题的:
```{r}
sevenseven <- ymd("2021-07-07")
sevenseven
typeof(sevenseven)
class(sevenseven)
```
注意这里打印出来的日期是符合阅读习惯的年月日,但是属于`Date`的class又是`double`的类别,也就意味着可以把这个日期当作一个单纯的数来计算。比如七月七日加上一天就是七月八日:
```{r}
sevenseven + 1
```
七月七日加上一个月就是八月七日:
```{r}
sevenseven + months(1)
```
年月日`ymd`函数所做的只是把输入的字符串自动识别并输出日期格式的数值,只要输入的字符串符合“年月日”的类似格式顺序。如果字符串不是年月日的格式,也没关系,`lubridate`也提供相应的 月年日`myd`,日月年`dmy`,月日年`mdy`,日年月`dym`,甚至是 年季`yq` 的函数。
`lubridate`的更多用法详见[`lubridate`主页](https://lubridate.tidyverse.org/)。
### 时间序列ts
时间序列作为一种有自相关性质的特殊数据类型在R中也是可以分开处理的。制造时间序列的函数叫做`ts`也就是time series的缩写
```{r}
xts <- ts(rnorm(12), start = c(2021, 1), frequency = 4)
xts
```
在这里创造的序列便拥有了时间序列的性质。`ts`函数的`start`参数设定了时间序列开始的时间,`frequency`参数设定了时间序列的周期性。在上面的例子中我们创造了一个从2021年第一季度开始的具有季节性的时间序列跨度三年。我们也有相应的函数可以提取这些时间序列的信息
```{r}
# 起始日期
start(xts)
# 结束日期
end(xts)
# 周期性
frequency(xts)
```
使用时间序列的好处在于我们可以用一些很简单的命令来使用时间序列的模型,比如使用`forecast`包来用一个ARIMA模型对澳大利亚燃气月生产量进行预测
```{r}
library(forecast)
gas %>%
auto.arima() %>%
forecast(36) %>%
autoplot()
```
关于时间序列的分析与预测的更多信息可见[`tidyverts`系列包](https://tidyverts.org/) [`forecast`包](https://pkg.robjhyndman.com/forecast/)等。
# 多维数据类型
之前我们讨论的数据类型都是一个序列(向量),都是一维的数据。在这章里我们会学习二维甚至多于二维的数据类型。
## 矩阵matrix
在R中的矩阵和数学概念上的矩阵很相似。在数学概念里矩阵是一个按照长方阵列排列的数字集合它有着固定的行数和列数。在R里矩阵是一个按照长方阵列排列的、有着固定行数和列数的、包含同一类型数据的集合。你可以使用函数`matrix`来创建一个矩阵:
```{r}
matrix(1:9, nrow = 3)
```
在这里,第一个参数是矩阵中数据的具体内容。`1:9` 是 `c(1, 2, 3, 4, 5, 6, 7, 8, 9)` 的一个缩写用于创建间隔为1的整数序列。
第二个参数告诉R这个矩阵应该有多少行。你也可以使用`ncol`来告诉R这个矩阵有多少列。默认状态下R会把数值按照从上到下、从左到右的顺序填充在这个固定行数列数的矩阵里。如果你想让R先从左到右填充横向按照行填充则需要将`byrow`参数设置为`TRUE`
```{r}
matrix(1:9, ncol = 3, byrow = TRUE)
```
R中的矩阵不局限于数值型矩阵它只要求包含的数据从属于同一类型如果是数值型那每一个格子里都是数值型如果是字符型所有值都是字符型数据。
```{r}
mat_month <- matrix(month.name, nrow = 4, byrow = TRUE)
mat_month
```
### 矩阵命名
对于一个矩阵来说,主要的命名集中于行名`rownames`和列名`colnames`
```{r}
# 你可以用这两个函数去更改行名和列名
rownames(mat_month) <- c("Quarter1", "Quarter2", "Quarter3", "Quarter4")
colnames(mat_month) <- c("Month1", "Month2", "Month3")
mat_month
# 也可以用这两个函数去获取行名和列名
rownames(mat_month)
colnames(mat_month)
# 或者用一个函数获取所有维度的名称
dimnames(mat_month)
```
### 访问矩阵子集
和在向量里一样,访问矩阵的子集也可以用`[`或者`[[`。区别在于矩阵中我们有两个维度,所以需要同时给定两个维度的坐标:
```{r}
# 访问矩阵中第1行第2列格子的元素
mat_month[[1, 2]]
# 在逗号前不输入数字的时候
# 根据列号截取整列
mat_month[, 2]
# 在逗号后不输入数字的时候
# 根据行号截取整行
mat_month[1, ]
# 如果有行名和列名的话
# 也可以用字符串来截取特定范围
mat_month[["Quarter1", "Month3"]]
```
## 列表list
列表是R中比较基础的数据类型中最灵活的类型。它和向量或者矩阵不一样在一个列表中可以储存各种不同的基本数据类型。你既可以存三个数字也可以把数值型、字符型、逻辑型混合
```{r}
list(1, 2, 3)
list(1, "lol", TRUE)
```
列表甚至可以储存列表本身,也就意味着你可以一层套一层地设置列表。夹杂其他各种类型,就可以创造一个庞然大物:
```{r}
stuff <- list(
list(
1:12,
"To be or not to be",
c(TRUE, FALSE)),
42,
list(
list(
ymd("2021-07-07"),
"remembrance"),
2L+3i)
)
stuff
```
### 访问子列表
列表同样可以用中括号来访问子列表。单个中括号`[`和两个中括号`[[`的区分在列表中特别重要。简单来说,单个中括号返回的列表元素类型还是列表,双中括号返回的列表元素是它本身的类型。想要返回多个子列表,就只能用单括号了,因为元素本身的类型不允许多个类型在一个序列中保存。
```{r}
# 返回前两个子列表
stuff[1:2]
# 返回第一个子列表中的第二个子列表
stuff[[1]][[2]]
```
### 列表命名
列表的维度,或者说层数可是比矩阵多多了,这也就意味着,列表中可以命名的地方多多了。
```{r}
# 给列表的顶层三个列表命名
names(stuff) <- c("I", "II", "III")
# 给列表的第一个列表里的三个子列表命名
names(stuff[[1]]) <- c("I", "II", "III")
```
如果列表有名字,自然可以用包含名字的字符串获取子列表。
```{r}
# 访问名为“I”的列表中名为“II”的子列表
stuff[["I"]][["II"]]
```
之前我们一直没有使用过美元符号`$`来获取子集,列表提供了一个最佳的展示场景,以下这行代码可以起到于上一行代码一样的效果,而不用加各种括号和引号:
```{r}
stuff$I$II
```
## 数据表data frame与tibble
数据表将是进行数据分析的时候接触的最多的数据类型了。一个数据表data frame的本质是一个列表list但是采取了矩阵matrix的展示形式
```{r}
df <- data.frame(x = 1:12, y = month.abb, z = month.name)
df
```
数据表的每一列是一个子列表。将几个长度相同的子列表并排放在一起,就组成了一个长方形的矩阵形式。这种特殊的处理使得数据表包含了两种数据形式的优势。列与列之间可以使用不同的基础数据类型,也就是说一列的数据是数值型的数据,下一列数据可以是字符型的数据。长方形的形状保证了列与列之间的数值是一一对应的,每一行都是一个观察量。这很符合日常会遇到的数据的形式。
`tibble`是`tidyverse`系列包中的`tibble`包提供的一种数据形式。使用`tibble`比较明显的好处是,当你把`tibble`打印在控制台里的时候它有一个更干净直观的打印方式。与data frame试图打印所有的行、一股脑把所有信息扔给你不同`tibble` 默认只会打印前几行给你一个数据长什么样的感觉,还会告诉你每一列的数据是什么类型的:
```{r}
tb <- tibble(a = 1:100, b = 101:200)
tb
```
除了看起来好看以外,`tibble`在原始数据表的基础上保留了有用的功能,去除了多余的功能。它干得更少,比如它不会自发修改变量类型或变量名字,也不会做部分匹配;同时它抱怨得更多,比如当一个变量不存在的时候就会触发错误信息。这样用户就能及早发现错误,不会等到代码堆成小`r emo::ji("poop")`山。
### 访问数据表内容
既然看上去像矩阵,听起来像列表,那就应该可以用适用于矩阵和列表的方法访问数据表元素。事实上也的确是这样:
```{r}
# 访问数据表名为x的列
df[["x"]]
df$x
# 访问第一行第二个数值
df[1, 2]
# 访问tibble第2列
tb[, 2]
# 访问tibble第1行第2列的数值
tb[1, 2]
```
```{r, eval = FALSE}
tb$a
#太长了还是不显示了吧
```
tibble的另一个特性是其访问的子列表也是`tibble`类型的数据表,即使是用单引号返回一个格子的元素。
关于`tibble`更多信息,详见[`tibble`主页](https://tibble.tidyverse.org/)。
# 读写数据
这一章我们主要讨论根据不同数据保存方式区分的读写数据的方法。
## 内置数据集
R本身和一些R包都会有内置的数据集。使用`data`命令来查看、使用可用数据集。
```{r, eval = FALSE}
# 查看R本身自带的数据集
data()
# 查看某一R包自带的数据集
data(package = "dplyr")
```
```{r}
# 载入AirPassengers数据集
data("AirPassengers")
glimpse(AirPassengers)
```
## 表格类型数据csv, excel)
h1n1流感问卷数据储存在名为“h1n1_flu.csv”的文件中我们会在下一篇《数据清洗与准备》中用到。假设“h1n1_flu"有不同的储存类型,我们列举一些读写数据表类型数据的方法。
```{r, eval = FALSE}
# 读取csv文件
library(readr)
h1n1_flu <- read_csv("h1n1_flu.csv")
# 保存csv文件
write_csv(h1n1_flu, "h1n1_flu.csv")
# 读取excel文件
library(readxl)
# 自动识别文件后缀
h1n1_flu <- read_excel("h1n1_flu.xls")
# 读取xls文件
h1n1_flu <- read_xls("h1n1_flu.xls")
# 读取xlsx文件
h1n1_flu <- read_xlsx("h1n1_flu.xlsx")
```
不建议在R中直接编辑excel文件csv文件应该满足日常所需了。如果有编辑excel文件的需求可以看看`openxlsx`包。
## R的专属类型数据RData, rds
有一些数据存储方式是R中独有的。我们在这里讨论两类。一类是rds文件一类是RData文件。
1. rds文件储存一个R中的对象。这个对象不一定是四四方方的数据表而可以是任何形式包括复杂的列表等。因为他储存的是一个对象所以读取的时候也是读取出来一个对象需要被保存在一个名字下。
1. RData储存的是一个或多个、任意结构的、带有自己名字的对象。读取的时候会将储存的对象直接载入当前的环境中使用的是对象自己的名字所以不需要再额外起名字。
```{r, eval = FALSE}
# 读取
h1n1_flu <- read_rds("h1n1_flu.rds")
# 存储
write_rds(h1n1_flu, "h1n1_flu.rds")
# 读取
load("h1n1_flu.RData")
# 存储
save(h1n1_flu, file = "h1n1_flu.RData")
```
## 其他软件SPSS, Stata, SAS
R也可以直接读取其他软件的数据类型。这里列举使用`haven`包读写SPSS的sav和zsav、Stata的dta、SAS的sas7bdat和sas7bcat。
```{r, eval = FALSE}
library(haven)
# SPSS
read_spss()
write_spss()
# Stata
read_dta()
write_dta()
# SAS
read_sas()
write_sas()
```
# 练习题
## 了解数据集
请使用之前读取的`h1n1_flu`完成以下任务。
### 常用数据探查函数
请尝试使用以下常用的数据探查函数,挑出两个你最喜欢的描述他们的功能。别忘了可以用`?fun`查看帮助文档。
```{r, eval = FALSE}
glimpse(h1n1_flu)
str(h1n1_flu)
head(h1n1_flu)
tail(h1n1_flu)
View(h1n1_flu)
summary(h1n1_flu)
nrow(h1n1_flu)
length(h1n1_flu$sex)
class(h1n1_flu$sex)
summary(h1n1_flu)
table(h1n1_flu$sex)
```
### 分组计算统计量
```{r, include = FALSE}
h1n1_flu <- read_csv("./datasets/h1n1_flu.csv")
```
```{r}
h1n1_flu %>%
group_by(sex, employment_status) %>%
summarise(n())
```
请问上边这几行代码在计算什么?你可不可以使用同样的方法计算一些其他的统计量?别忘了看看帮助文档`?summarise`。
## 创造数据集
我们说过数据表的本质是将列表排列在一起,所以数据表就会有列表的性质。而我们又知道列表可以包含任何类型的数据,无论是单个的数值或者是向量、矩阵等。
1. 请你创造一个数据表,其中的某一列变量的每一个格子包含的不再是常规的单个数值或者字符串,而是一个向量或者矩阵等多维的数据类型;
1. 请你描述一个可以在数据分析时运用此类特性的使用场景。
----
By: Fin
> https://yangzhuoranyang.com
关于Datawhale Datawhale是一个专注于数据科学与AI领域的开源组织汇集了众多领域院校和知名企业的优秀学习者聚合了一群有开源精神和探索精神的团队成员。Datawhale 以“for the learner和学习者一起成长”为愿景鼓励真实地展现自我、开放包容、互信互助、敢于试错和勇于担当。同时 Datawhale 用开源的理念去探索开源内容、开源学习和开源方案,赋能人才培养,助力人才成长,建立起人与人,人与知识,人与企业和人与未来的联结。 本次数据挖掘路径学习专题知识将在天池分享详情可关注Datawhale
[![logo.png](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)

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---
title: |
| DataWhale 组队学习 R语言数据分析
| Task02 数据清洗与准备
author: "June Yao"
date: "`r Sys.Date()`"
header-includes:
- \usepackage{ctex}
urlcolor: blue
output:
prettydoc::html_pretty:
theme: cayman
highlight: github
number_section: no
toc: no
knit: (function(inputFile, encoding) {
rmarkdown::render(inputFile, encoding = encoding,
output_dir = "output", output_format = "all") })
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,warning=FALSE, message=FALSE,tidy=TRUE,collapse=FALSE)
```
![](./image/task02_structure.jpg){width=100%}
Task02共计6个知识点预计需学习5~8小时请安排好学习任务。
## 0 环境配置
```{r}
library(mlbench) #将会使用到包中的BostonHousing数据集
library(funModeling) # 探索性数据分析工具包本节内容中将会使用到它的status()函数,打印整体数据质量
library(tidyverse) # 数据转化工具包本节内容中将会使用它包含的dplyr中的管道函数 %>%
library(VIM) # 缺失值可视化工具包本节内容中将会使用到它的aggr()函数
library(mice) #缺失值处理工具包,本节内容会使用它来进行多重插补
library(Rlof) #用于LOF异常值检测方法本节内容将会使用到它的lof()函数
library(fastDummies) #用于生成dummy的包本节内容将会使用到它的dummy_cols()函数
library(sjmisc) #用于生成dummy的包本节内容将会使用到它的to_dummy()函数
library(MASS)#基于此包进行box-cox转换
library(dlookr) #本节内容将会使用到它的transform()函数
```
## 0 案例数据
本节内容将会使用到两个数据集。
### 数据集1 h1n1流感问卷数据集
#### 数据说明
目前提供的数据集来自关于h1n1流感调查问卷的部分内容可以从这个网站上看到具体字段的详细说明https://www.drivendata.org/competitions/66/flu-shot-learning/page/211/
数据集包含26,707个受访者数据共有32个特征+1个标签是否接种h1n1疫苗
#### 加载并查看部分数据
首先加载数据,了解数据集大小。
```{r h1n1}
h1n1_data <- read.csv("./datasets/h1n1_flu.csv", header = TRUE)
dim(h1n1_data)
```
为了简化本章的示例我们在这32个特征中筛选出了10个特征作为一个子集来学习如何使用R做数据清洗与准备。如有兴趣可以把下面这块筛选去掉自己用完整数据集做一次探索。
```{r }
h1n1_data <- h1n1_data[,c(1,3,11,12,15,16,19,20,22,23,33)]
head(h1n1_data)
```
### 数据集2 波士顿房价数据集
#### 数据说明
数据集来自`mlbench`包请提前装好。数据字段说明可从网址查看https://blog.csdn.net/weixin_46027193/article/details/112238597
数据集包含506条房价信息共有13个特征+1个预测字段房屋价格
#### 加载并查看部分数据
```{r }
data(BostonHousing)
dim(BostonHousing)
head(BostonHousing)
```
## 1 重复值处理
在某些情况下,我们需要对数据进行去重处理。`unique()`函数可以对数据进行整体去重,`distinct()`函数可以针对某些列去重。
```{r }
#整体去重
h1n1_data_de_dup1 <- unique(h1n1_data)
#指定根据列respondent_id,h1n1_knowledge去重并保留所有列
h1n1_data_de_dup2 <- distinct(h1n1_data,respondent_id,h1n1_knowledge,.keep_all = T)
```
## 2 缺失值识别与处理
现实环境中,由于数据来源及搜集过程,可能有各种不规范,导致数据往往会存在缺失。缺失值识别与处理,无论是在统计还是数据管理中,往往是数据清洗的第一步。
### 2.1 缺失值识别
#### 2.1.1 常用识别方法
在R语言中惯用会把缺失值表示为NA一般可使用`is.nan(a)``!complete.cases(a)`来识别`a`是否为缺失值。
```{r }
#假设定义的一个变量中存在缺失值
y <- c(1, 2, 3, NA)
#用is.nan在识别是否为缺失值
is.na(y)
#用!complete.cases()在识别是否为缺失值
!complete.cases(y)
```
#### 2.1.2 缺失值统计
统计缺失值总数。
```{r }
# 数据集中总缺失数据量
sum(is.na(h1n1_data))
# 数据集中某一列缺失数据量
sum(is.na(h1n1_data["h1n1_knowledge"]))
```
如果想按行或按列统计,可以写函数。
```{r }
pMiss <- function(x){sum(is.na(x))/length(x)*100}
apply(h1n1_data,2,pMiss) #按列统计缺失比率%
# apply(h1n1_data,1,pMiss) #按行统计缺失比率%
```
或调用一些现成的包。比如,我们可以使用`funModeling`包中的`status()`函数直接观测案例数据中包含的0值缺失值NA在每个特征中的分布情况。以h1n1 flu数据集为例
```{r }
data_quality <- status(h1n1_data)
data_quality %>% mutate(across(where(is.numeric), ~ round(., 3))) #保留4位小数
```
结合案例数据h1n1 flu来看存在缺失值的有5个特征字段。
```{r}
missing_Value <- data_quality[which(data_quality$p_na > 0), ]
missing_Value$variable
```
#### 2.1.3 缺失值机制与分析
统计学家通常将缺失数据分为3类为了更好的处理缺失值我们可以基于缺失值机制来识别以下3种缺失模式
* MCAR完全随机缺失如果数据的缺失与任何值观察或缺失之间没有关系则为MCAR。
* MAR随机缺失考虑MAR与MCAR有何不同如果缺失和观测值之间存在系统关系则为MAR。例如-男性比女性更容易告诉自己的体重因此体重就是MAR。“ Weight”变量的缺失取决于变量"Sex"的观测值。
* MNAR非随机缺失若缺失数据不属于MCAR和MAR数据的缺失依赖于不完全变量本身则数据为非随机缺失。例如抑郁程度高的人更不容易填写抑郁调查问卷。
MNAR是最复杂的情况处理 MNAR的策略是找到更多有关缺失原因的数据或者执行假设分析查看结果在各种情况下的敏感程度。大部分处理缺失数据的方法都假定数据是MCAR或MAR此时可以忽略缺失数据的生成机制在替换或删除缺失数据后直接对感兴趣的关系进行建模。
以下介绍几种可视化分析缺失数据关联的方法:
我们用`VIM`包里的`aggr()`函数,直观看一下具体的缺失情况。
```{r }
aggr(h1n1_data,cex.axis=.6, oma = c(9,5,5,1)) #cex.axis调整轴字体大小oma调整外边框大小
```
通过用`VIM`包里的矩阵图`matrixplot()`函数,可以检查某些变量的缺失值模式是否与其他变量的真实值有关联。矩阵图中,观测数据以黑白色阶显示(颜色越深,数值越高),缺失值会被标记为红色。我们对某一个存在缺失值的变量进行排序,来找寻含缺失值变量与其他变量的关系。
在此案例中,我们按照`health_insurance`进行分组排序。可以看到是否有慢性病`chronic_med_condition`的缺失,与`opinion_h1n1_vacc_effective`的缺失相对较集中。除此之外,也可以看到有慢性病的人年龄普遍较大。
```{r }
#先简单处理一下一些类别变量的顺序
h1n1_data_matplt <- h1n1_data
h1n1_data_matplt$age_group <- factor(h1n1_data_matplt$age_group)
h1n1_data_matplt$education <- factor(h1n1_data_matplt$education,levels = c("", "< 12 Years", "12 Years","Some College","College Graduate"))
h1n1_data_matplt$sex <- factor(h1n1_data_matplt$sex)
h1n1_data_matplt$income_poverty <- factor(h1n1_data_matplt$income_poverty,levels = c("18 - 34 Years", "<= $75,000, Above Poverty", "> $75,000"))
# levels(h1n1_data_matplt$age_group) # 查看顺序
#矩阵图可视化
par(mar=c(9, 4.1, 2.1, 2.1)) # x轴标签太长调用par()函数调整外边框的大小
matrixplot(h1n1_data_matplt, sortby = "chronic_med_condition",cex.axis=0.7) #cex.axis为调整坐标轴字体大小
```
用相关性探索缺失值。首先生成一个影子矩阵用指示变量替代数据集中的数据1表示缺失0表示存在
```{r }
shadow_mat <- as.data.frame(abs(is.na(h1n1_data[,-1])))
head(shadow_mat)
```
```{r }
# 可提取含缺失值的变量
shadow_mat <- shadow_mat[which(apply(shadow_mat,2,sum)>0)]
# 计算相关系数
cor(shadow_mat)
# 相关系数热力图
heatmap(cor(shadow_mat) )
```
根据缺失相关性矩阵,`opinion_h1n1_vacc_effective ` 与 `chronic_med_condition` 缺失相关性较大。
综上在案例中变量之间的存在部分相关性考虑为MAR。
其他数据缺失关系分析,可参考附录`数据的预处理基础`。
### 2.2 缺失值处理
缺失值一般有三种方式:
* 将缺失值作为变量值使用。比如在民意调查中,当选民不投票时,可以将缺失值处理为"无法确定"。
* 删除数据。主要有删除样本值和删除特征值。但可能会损失掉一些有用信息。
* 插补法。如均值/中位数/同类均值插补(数值变量),众数插补(类别变量),手动插补(根据主观理解),多重插补等。
以下我们主要介绍删除法和插补法:
#### 2.2.1 删除法
行删除,可以直接用`complete.cases()`或`na.omit()`来过滤掉数据集中所有缺失行。
```{r }
h1n1_data_row_del1 <- h1n1_data[!complete.cases(h1n1_data),]
h1n1_data_row_del2 <- na.omit(h1n1_data)
```
列删除,一般对于缺失率极高又没有太大作用的特征值,我们直接删除,如可以用`dataset[,-5]`去掉第五列,或` subset(dataset, select = -c(col1, col2))`去掉列col1和列col2。
比如,我们把`health_insurance`变量删除。
```{r }
h1n1_data_col_del1 <- subset(h1n1_data,select = -c(health_insurance))
```
#### 2.2.2 简单插补法
注意在空值插补的时候,要区分类别变量与数值变量,均值插补不适用于类别变量。我们这里随机选择了一个变量演示`impute()`函数用法,在实际插补的时候,请大家根据情况进行选择。
```{r }
h1n1_data_sim_imp <- h1n1_data
h1n1_data_sim_imp$h1n1_knowledge <- impute(h1n1_data_sim_imp$h1n1_knowledge, 1) #填充特定值
h1n1_data_sim_imp$h1n1_knowledge <- impute(h1n1_data_sim_imp$h1n1_knowledge, median) #插补中位数
h1n1_data_sim_imp$h1n1_knowledge <- impute(h1n1_data_sim_imp$h1n1_knowledge, mean) #插补均值
```
#### 2.2.3 拟合插补法
利用有监督的机器学习方法,比如回归、最邻近、随机森林、支持向量机等模型,对缺失值作预测。
#### 2.2.4 多重插补法
多重插补MI是一种基于重复模拟的处理缺失值的方法。其思想来源于贝叶斯估计认为待插补的值是随机的它的值来自于已观测到的值。具体实践上通常是估计出待插补的值然后再加上不同的噪声形成多组可选插补值通常是3到10个。根据某种选择依据选取最合适的插补值。与单个插补例如均值相比创建多个插补可解决缺失值的不确定性。 R中可利用`Amelia`、`mice`和`mi`包来执行这些操作。
本节中我们将用案例介绍mice包通过链式方程进行的多元插补提供的方法。使用mice生成m个完整的插补数据集。然后利用`with-pool`的方法来评估选择哪一个数据集。首先使用`with()`函数依次对每个完整数据集应用统计模型如lmglm等用`summary()`输出数据集检验,看某数据集是否合格。接下来`pool()`函数把5个回归模型汇总用`summary()`输出汇总数据集检验,查看整体插补方法是否合格。检验结果分析可参考附录`mice检验结果解释`
![](./image/task02_mice.jpg){width=60%}
```{r }
#先处理下数据,把数据集中一些类别变量转换回来
#imp是一个包含m个插补数据集的列表对象同时还含有完成插补过程的信息。
#参数m的默认值为5这里我们将m设为4生成4个无缺失数据集
#参数method, 对于每个变量的拟合,可以指定所用的拟合方法,method传入的参数可以是一个具体方法也可以为不同列指定具体方法具体方法选择可参考附录mice使用文档。这里我们使用默认值。
imp <- mice(h1n1_data,m=4,seed=122,printFlag=FALSE)
#查看变量h1n1_knowledge在几个插补数据集中的插补结果
# imp$imp$h1n1_knowledge
#查看每个变量所用的插补方法
# imp$method
#设定应用于m个插补数据集的统计分析方法。方法包括做线性回归模型的lm()函数、做广义线性模型的glm()函数、做广义可加模型的gam()做负二项模型的nbrm()函数
fit <- with(imp, lm(h1n1_vaccine~h1n1_knowledge + doctor_recc_h1n1 + chronic_med_condition + health_insurance + opinion_h1n1_vacc_effective))
# 输出每个数据集检验
print.data.frame(summary(fit),digits=4)
#包含m个统计分析平均结果的列表对象
pooled <- pool(fit)
#这是一个总体评估结果
pooled
#这里修改action的参数范围1-m选择一个数据集作为我们已填充完成的数据集
h1n1_data_complete <- complete(imp, action=2)
```
## 3 异常值识别与处理
### 3.1 异常值识别
本节的异常值指离群点。为了让数据统计或数据建模更加准确,我们通常会识别并对处理一些离群点。有些模型会对异常值较敏感,参考附录`什么样的模型对缺失值更敏感?`。
总的来说有几种常用方法包括可视化图形分布识别箱线图、z-score识别、局部异常因子法LOF法、聚类法等。
我们这里用波士顿房价数据集来演示一下异常值识别的处理过程。
### 3.1.1 可视化图形分布
首先是可视化图形分布识别将数值型变量筛选出来用boxlpot看看分布。
```{r }
#提取数值字段
nums <- unlist(lapply(BostonHousing, is.numeric))
nums_data<-BostonHousing[ , nums]
#数据变形
nums_data.new <- nums_data %>%
as.data.frame %>%
mutate(Cell= rownames(.)) %>%
gather(., key= colname, value="value", -Cell)
#用ggplot画出箱线图
ggplot(data = nums_data.new, aes(x = colname, y = value)) + geom_boxplot(aes(1)) +
facet_wrap(~colname, scales = "free") + theme_grey() + labs(title = "Outlier Detection On Numeric Data By Boxplot", x = "Numeric Columns", y = "") + theme(legend.position = "top") + theme_bw()
```
通过可视化分布可以选择剔除一些不合理的离群值比如在数据集中将dis>10.0的数据剔除。
### 3.1.2 z-score
z-score是一种一维或低维特征空间中参数异常检测方法。它假定数据是高斯分布异常值是分布尾部的数据点因此远离数据的平均值。一般将z-score低于-3或高于3的数据看成是异常值。
```{r }
#定义一个识别异常点的函数x是输入数据matrix或df,zs是异常临界值z-score超过zs的被识别为异常点
outliers = function(x, zs) {
temp <- abs(apply(x, 1, scale ))
return(x[temp > zs])
}
#打印出z-score<3的值
outliers(nums_data, 3)
```
### 3.1.3 局部异常因子法
局部异常因子法(LOF),是一种无监督的离群检测方法,是基于密度的离群点检测方法中一个比较有代表性的算法。适用于在中等高维数据集上执行异常值检测。
```{r }
# k是计算局部异常因子所需要判断异常点周围的点的个数
outlier_score <- lof(data=nums_data, k=5)
# 绘制异常值得分的直方分布图
hist(outlier_score, col = "#8ac6d1")
# 排序,挑出得分排前五的数据(找到索引)作为异常值
names(outlier_score) <- 1:nrow(nums_data)
sort(outlier_score, decreasing = TRUE)[1:5]
```
### 3.2 异常值处理
首先需要确定是否是真的异常值,有些值虽然离群,但其实并不是异常值,处理掉反而会影响后续任务的准确性。 如果确定需要处理,可以参考缺失值的处理方式进行处理。
## 4 特征编码
为什么要进行特征编码?我们拿到的原始数据中,一般会有一些类别变量,但是在统计或机器学习中,我们通常需要把类别变量转化为数值型变量,才能应用于一些方法中。
### 4.1 独热编码/哑编码
One-hot encoding 和 dummy,是将类别变量扩充为多个只显示10的变量每个变量代表原类别变量中的一个类。 注意他们之间的区别https://www.cnblogs.com/lianyingteng/p/7792693.html
* 优点解决了分类器不好处理分类数据的问题在一定程度上也起到了扩充特征的作用。它的值只有0和1不同的类型存储在垂直的空间。
* 缺点:当类别的数量很多时,特征空间会变得非常大,容易造成维度灾难。(为避免维度灾难,后续可以考虑降维处理)
R里面有很多现成的转化编码的包我们这里使用了`dummy_cols()`函数做演示可以看到原来的类别类型字段已经扩充为多个01编码的字段。
```{r }
h1n1_data_dummy <- dummy_cols(subset(h1n1_data_complete, select = c(age_group)), select_columns = c("age_group"))
head(h1n1_data_dummy)
```
### 4.2 标签编码
标签编码(Label Encoder)是将类别变量转换成连续的数值型变量,通常对有序的变量进行标签编码,既保留了顺序信息,也节约了空间(不会扩充变量)
R里有一个特殊的结构factorfactor是有序的分类变量我们这里可以利用factor来做标签编码。首先根据实际情况设置factor的类别顺序然后直接用`as.numeric()`转化为数字。
```{r }
h1n1_data_complete_lab_encoder <- h1n1_data_complete
h1n1_data_complete_lab_encoder$income_poverty_lab_encoder <-as.numeric(factor(h1n1_data_complete_lab_encoder$income_poverty, levels = c("Below Poverty", "<= $75,000, Above Poverty", "> $75,000")))
head(subset(h1n1_data_complete_lab_encoder, select = c(income_poverty,income_poverty_lab_encoder)))
```
### 4.3 手动编码
比如,当某一个特征中有很多类别,我们认为某些类别可以合为一类,可以用`case_when()`函数手动处理。
```{r }
h1n1_data_manual<-subset(h1n1_data_complete, select = c(age_group))
h1n1_data_manual$age_group_manual<-case_when(
h1n1_data_manual$age_group %in% c("18 - 34 Years") ~ 1,
h1n1_data_manual$age_group %in% c("35 - 44 Years","45 - 54 Years","55 - 64 Years") ~ 2,
h1n1_data_manual$age_group %in% c("65+ Years") ~ 3
)
head(h1n1_data_manual)
```
### 4.4 日期特征转换
参考附录`R语言日期时间处理`
## 5 规范化与偏态数据
为什么要数据规范化简单来说是为了去除数据量纲和数据大小的差异确保数据是在同一量纲或者同一数量级下进行比较一般用在机器学习算法之前。数据规范化又可以使用0-1规范化Z-score等方法。
为什么要处理偏态数据?。很多模型会假设数据或参数服从正态分布。例如线性回归(linear regression),它假设误差服从正态分布。
提示:注意在测试数据与训练数据分布差别很大的情况下,对测试数据运用一些规范化方法时,可能因为数据分布不匹配而带来误差。
这里我们使用波士顿房价数据集来做演示。可以看到图中数据的偏态分布及量纲差别。
```{r }
BostonHousing %>% keep(is.numeric) %>%
gather() %>% ggplot(aes(value)) +
facet_wrap(~key,scales = "free") +
geom_density(color="#348498",fill="#8ac6d1") + theme_bw()
```
### 5.1 0-1规范化
0-1规范化是将原始数据缩放到[0,1]区间内,一般方法是最小最大规范的方法,公式如下:
![](./image/task02_0-1norm.png){width=20%}
这里用循环计算出每一列的最大最小值,再根据公式求出缩放后的数据。
```{r }
nums_data_norm1 <- nums_data
for (col in names(nums_data_norm1))
{
xmin<-min(nums_data_norm1[col])
xmax<-max(nums_data_norm1[col])
nums_data_norm1[col]<-(nums_data_norm1[col]-xmin)/(xmax-xmin)
}
head(nums_data_norm1)
```
转换完再看一下分布已经缩放到0-1之间了。
```{r }
nums_data_norm1 %>% keep(is.numeric) %>%
gather() %>% ggplot(aes(value)) +
facet_wrap(~key,scales = "free") +
geom_density(color="#348498",fill="#8ac6d1") + theme_bw()
```
此外可以用dlookr包里的`transform()`函数。
```{r }
nums_data_norm2 <- nums_data
nums_data_norm2$crim <- dlookr::transform(nums_data$crim,method = "minmax")
```
### 5.2 Z-score标准化
Z-score标准化是原数据减去期望再除以标准差将数据按比例缩放使其落入到一个小的区间内标准化后的数据可正可负但是一般绝对值不会太大。
![](./image/task02_z-score.png){width=15%}
R里面可以用`scale()`函数来计算z-score。也可以dlookr包里的中`transform()`函数。
```{r }
nums_data_zscore <- nums_data
nums_data_zscore <- scale(nums_data_zscore)
head(nums_data_zscore)
```
转换完再看一下分布数据缩放后在0周围的一个小区间了。
```{r }
data.frame(nums_data_zscore) %>% keep(is.numeric) %>%
gather() %>% ggplot(aes(value)) +
facet_wrap(~key,scales = "free") +
geom_density(color="#348498",fill="#8ac6d1") + theme_bw()
```
### 5.3 对数转换(log transform)
使用对数转换也是一种常见的处理偏斜特征的方法但要注意原数据中不能含有负值。此外为了避免0值我们通常使用log1p公式为`lg(x+1)`。可以直接用dlookr包里的`transform()`函数一般结合mutate函数一起使用。
```{r }
#直接公式转换
nums_data_log1p1 <- log(nums_data+1)
#用transform()函数
nums_data_log1p2 <- nums_data
nums_data_log1p2$b <- dlookr::transform(nums_data_log1p2$b,method = "log+1")
```
转换完再看一下分布,大多变量转换后接近正态分布了。但是这里要特别注意离散数据。
```{r }
nums_data_log1p1 %>% keep(is.numeric) %>%
gather() %>% ggplot(aes(value)) +
facet_wrap(~key,scales = "free") +
geom_density(color="#348498",fill="#8ac6d1") + theme_bw()
```
### 5.4 Box-Cox
Box-Cox变换是Box和Cox在1964年提出的一种广义幂变换方法在变换后可以一定程度上减小不可观测的误差和预测变量的相关性在机器学习中经常用来处理偏态分布。其一个显著优点是通过求变换参数来确定变换形式而这个过程完全基于数据本身而无须任何先验信息这无疑比凭经验或通过尝试而选用对数、平方根等变换方式要客观和精确。计算公式如下
![](./image/task02_boxcox.png){width=40%}
示例参考附录`基于R语言进行Box-Cox变换`
## 6 小拓展
R语言中mutate 类似于SQL中根据表的现有变量生成新变量。使用mutate集中处理变量转换代码显示较整洁。
```{r }
h1n1_data_de <- h1n1_data_complete %>% to_dummy(education, suffix = "label") %>%
bind_cols(h1n1_data_complete) %>%
mutate(
#标签编码(label encoder)
sex = as.factor(as.numeric(factor(sex))),
income_poverty = (as.numeric(factor(
income_poverty,
levels = c(
"Below Poverty",
"<= $75,000, Above Poverty",
"> $75,000"
)
))),
#手动编码
age_group = as.factor(
case_when(
age_group %in% c("18 - 34 Years") ~ 1,
age_group %in% c("35 - 44 Years","45 - 54 Years","55 - 64 Years") ~ 2,
age_group %in% c("65+ Years") ~ 3
)),
#标准化
across(
c("h1n1_knowledge",
"doctor_recc_h1n1",
"chronic_med_condition",
"opinion_h1n1_vacc_effective",
"age_group",
"income_poverty"),
~ scale(as.numeric(.x))
)
) %>% dplyr::select(-one_of("education","education_"))
head( h1n1_data_de)
```
注意在机器学习中尽量在数据集划分后分别在训练集与验证集、测试集上进行数据清洗避免数据泄露。R中的数据集划分方法参考附录`R中数据集分割`。
## 思考与练习
看完了本节数据清洗与准备,尝试着选取一个完整的数据集(从本节中选取或使用自己的数据集),来做一次清洗吧!
## 附录:参考资料
### 理论资料
**数据的预处理基础:** 如何处理缺失值 https://cloud.tencent.com/developer/article/1626004
**多重插补法:** 处理缺失值之多重插补Multiple Imputationhttps://zhuanlan.zhihu.com/p/36436260
**异常值检测:** R语言--异常值检测 https://blog.csdn.net/kicilove/article/details/76260350
**异常值检测之LOF** 异常检测算法之局部异常因子算法-Local Outlier Factor(LOF) https://blog.csdn.net/BigData_Mining/article/details/102914342
**规范化:** 规范化、标准化、归一化、正则化 https://blog.csdn.net/u014381464/article/details/81101551
**什么样的模型对缺失值更敏感?:** https://blog.csdn.net/zhang15953709913/article/details/88717220
### R语言函数用法示例
`funModeling`用法示例https://cran.r-project.org/web/packages/funModeling/vignettes/funModeling_quickstart.html
`tidyverse`官方文档https://www.tidyverse.org/
`VIM`教学网页https://www.datacamp.com/community/tutorials/visualize-data-vim-package
`mice`使用文档(Multivariate Imputation by Chained Equations)https://cran.r-project.org/web/packages/mice/mice.pdf
`mice`使用中文解释https://blog.csdn.net/sinat_26917383/article/details/51265213
`mice`检验结果解释http://blog.fens.me/r-na-mice/
`caret`包数据预处理https://www.cnblogs.com/Hyacinth-Yuan/p/8284612.html
R语言日期时间处理https://zhuanlan.zhihu.com/p/83984803
基于R语言进行Box-Cox变换https://ask.hellobi.com/blog/R_shequ/18371
R中数据集分割https://zhuanlan.zhihu.com/p/45163182
**Task2 END.**
--- By: June
> 悉尼大学研究生Datawhale成员
关于Datawhale Datawhale是一个专注于数据科学与AI领域的开源组织汇集了众多领域院校和知名企业的优秀学习者聚合了一群有开源精神和探索精神的团队成员。Datawhale 以“for the learner和学习者一起成长”为愿景鼓励真实地展现自我、开放包容、互信互助、敢于试错和勇于担当。同时 Datawhale 用开源的理念去探索开源内容、开源学习和开源方案,赋能人才培养,助力人才成长,建立起人与人,人与知识,人与企业和人与未来的联结。 本次数据挖掘路径学习专题知识将在天池分享详情可关注Datawhale
[![logo.png](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)

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@ -0,0 +1,151 @@
---
title: |
| DataWhale 组队学习 R语言数据分析
| Task03 基础统计分析
author: "杨佳达"
date: "`r Sys.Date()`"
header-includes:
- \usepackage{ctex}
urlcolor: blue
output:
prettydoc::html_pretty:
theme: cayman
highlight: github
number_section: no
toc: no
knit: (function(inputFile, encoding) {
rmarkdown::render(inputFile, encoding = encoding,
output_dir = "output", output_format = "all") })
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,warning=FALSE, message=FALSE,tidy=TRUE,collapse=FALSE)
```
![](./image/task03_structure.png){width=100%}
# 基础统计分析
## 准备工作
如果没有相关的包,则使用`install.packages('package_name')`进行安装以下包。
```{r}
library(pastecs)
library(psych)
library(ggm)
```
读取数据使用H1N1流感数据集和波士顿房价数据集。
```{r}
flu = read.table('./datasets/h1n1_flu.csv', header=TRUE, sep=',')
housing = read.csv('./datasets/BostonHousing.csv', header=TRUE)
```
## 1 多种方法获取描述性统计量
### 1.1 基础方法
通过summary计算数值型变量的最大值、最小值、分位数以及均值类别变量计算频数统计。
```{r}
summary(flu[c("household_children","sex")])
```
```{r}
summary(flu[c("h1n1_concern", "h1n1_knowledge")])
```
通过 sapply() 计算描述性统计量,先定义统计函数,在进行聚合计算。
```{r}
mystats <- function(x, na.omit=FALSE){
if (na.omit)
x <- x[!is.na(x)]
m <- mean(x)
n <- length(x)
s <- sd(x)
skew <- sum((x-m)^3/s^3)/n
kurt <- sum((x-m)^4/s^4)/n - 3
return(c(n=n, mean=m, stdev=s, skew=skew, kurtosis=kurt))
}
sapply(flu[c("h1n1_concern", "h1n1_knowledge")], mystats)
```
### 1.2 拓展包方法
通过pastecs包中的 stat.desc()函数计算描述性统计量可以得到中位数、平均数、平均数的标准误、平均数置信度为95%的置信区间、方差、标准差以及变异系数。
```{r}
stat.desc(flu[c("household_children","sex")])
```
通过psych包中的describe()计算描述性统计量。
```{r}
describe(flu[c("household_children","sex")])
```
## 2 分组计算描述性统计
### 2.1 基础方法
#### 使用aggregate()分组获取描述性统计
1. 分组计算不同性别收入贫困计数。
2. 是否属于查尔斯河的房价中位数平均值。
```{r}
aggregate(flu[c("income_poverty")], by=list(sex=flu$sex), length)
aggregate(housing$medv, by=list(medv=housing$chas), FUN=mean)
```
#### 使用 by() 分组计算描述性统计量
```{r}
by(flu[c("income_poverty", "sex")], flu$sex, length)
```
## 3 频数表和列联表
```{r}
table(flu$sex)
```
## 4 相关
### 4.1 相关的类型
#### Pearson、Spearman和Kendall相关
R可以计算多种相关系数包括Pearson相关系数、Spearman相关系数、Kendall相关系数、偏相关系数、多分格polychoric相关系数和多系列polyserial相关系数。
1. 计算房价数据的相关系数默认是Pearson相关系数。
```{r}
cor(housing)
```
2. 指定计算Spearman相关系数
```{r}
cor(housing, method="spearman")
```
3. 城镇人均犯罪率与房价的相关系数
```{r}
x <- housing
y <- housing[c("medv")]
cor(x, y)
```
#### 偏相关
偏相关是指在控制一个或多个定量变量时另外两个定量变量之间的相互关系。使用ggm 包中的 pcor() 函数计算偏相关系数。
### 4.2 相关性的显著性检验
```{r}
cor.test(housing[,c("crim")], housing[,c("medv")])
```
## 5 方差分析
方差分析ANOVA又称“变异数分析”或“F检验”用于两个及两个以上样本均数差别的显著性检验。
### 5.1 单因素方差分析
从输出结果的F检验值来看p<0.05比较显著,说明是否在查尔斯河对房价有影响。
```{r}
fit <- aov(housing$medv ~ housing$chas)
summary(fit)
```
### 5.2 多因素方差分析
构建多因素方差分析,查看因子对房价的影响是否显著。
```{r}
fit <- aov(housing$medv ~ housing$crim*housing$b)
summary(fit)
```

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@ -0,0 +1,414 @@
---
title: |
| DataWhale 组队学习 R语言数据分析
| Task04 数据可视化
author: "牧小熊"
date: "`r Sys.Date()`"
header-includes:
- \usepackage{ctex}
urlcolor: blue
output:
prettydoc::html_pretty:
theme: cayman
highlight: github
number_section: no
toc: no
knit: (function(inputFile, encoding) {
rmarkdown::render(inputFile, encoding = encoding,
output_dir = "output", output_format = "all") })
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,warning=FALSE, message=FALSE,tidy=TRUE,collapse=TRUE)
```
![](./image/task04_structure.png){width=60%}
## 0.ggplot2包介绍
ggplot2包由Hadley Wickham编写提供了一种基于Wilkinson所述图形语法的图形系统。ggplot2包的目标是提供一个全面的、基于语法的、连贯一致的图形生成系统允许用户创建新颖的、有创新性的数据可视化图形。
总的来说有以下几点:
- ggplot2的核心理念是将绘图与数据分离数据相关的绘图与数据无关的绘图分离
- ggplot2保有命令式作图的调整函数使其更具灵活性
- ggplot2将常见的统计变换融入到了绘图中。
- ggplot2是按图层作图
ggplot2图像的三个基本构成数据、图形属性映射、几何对象
按照ggplot2的绘图理念Plot(图)= data(数据集)+ Aesthetics(美学映射)+ Geometry(几何对象)。
例如:
```{r example}
#ggplot(data,aes(x=x,y=y))+geom_point()
```
- 数据:用于绘制图形的数据
- 映射aes()函数是ggplot2中的映射函数, 所谓的映射即为数据集中的数据关联到相应的图形属性过程中一种对应关系, 图形的颜色,形状,分组等都可以通过通过数据集中的变量映射。
- 几何对象:我们在图中实际看到的图形元素,如点、线、多边形等。
ggplot2绘图代码如同数据公式一般只需要套相应的公式即可绘制出丰富的图形后续的讲解也会按照此方法。
ggplot2参考链接
- https://ggplot2.tidyverse.org/reference/
- https://ggplot2-book.org/
ggplot2的安装方法
```{r cars}
#install.packages("ggplot2")
```
## 1.环境配置
``` {r}
library(ggplot2) #画图工具ggplot2
library(ggpubr) #将多个图形拼接
library(plyr) #数据处理包
```
在本讲中会用到ggpubr中的ggrrange这个多图拼接工具详细使用方法参见
http://www.sthda.com/english/articles/24-ggpubr-publication-ready-plots/81-ggplot2-easy-way-to-mix-multiple-graphs-on-the-same-page/
## 案例数据
本节内容将会使用到两个数据集
**1.1h1n1流感问卷数据集**
h1n1流感问卷数据集是关于h1n1流感问卷调查的一个数据属于外部数据
数据集包含26,707个受访者数据共有32个特征+1个标签是否接种h1n1疫苗
读取相关的数据集
```{r h1n1}
h1n1_data <- read.csv("./datasets/h1n1_flu.csv", header = TRUE)
```
**1.2波士顿房价数据集**
波士顿房价数据集属于R语言自带数据集也可以通过外部读取
读取相关的数据集
```{r boston}
boston_data <- read.csv("./datasets/BostonHousing.csv", header = TRUE)
```
## 2.散点图
散点图是指在数理统计回归分析中,数据点在直角坐标系平面上的分布图,散点图表示因变量随自变量而变化的大致趋势,由此趋势可以选择合适的函数进行经验分布的拟合,进而找到变量之间的函数关系。
散点图的优势:
- 数据用图表来展示,显然比较直观,在工作汇报等场合能起到事半功倍的效果,让听者更容易接受,理解你所处理的数据。
- 散点图更偏向于研究型图表,能让我们发现变量之间隐藏的关系为我们决策作出重要的引导作用。
- 散点图核心的价值在于发现变量之间的关系,包括线性与非线性之间的关系。
```{r plot1}
#读取数据
boston_data <- read.csv("./datasets/BostonHousing.csv", header = TRUE)
#绘制简单的散点图 x轴选择的是lstat ,y轴选择的是medv
ggplot(data=boston_data, aes(x=lstat, y=medv)) + geom_point()
```
上图选择的是lstat为x轴medv为y轴绘制的散点图x轴表示弱势群体人口所占比例y轴表示房屋的平均价格通过图上的数据可以看到弱势人群的比例增加会影响房价这2个变量呈现一定的负相关。
ggplot2可以修改散点图的性状和大小,R语言中存储了一些相关的形状
![](./image/task04_fig1.png){width=50%}
size参数修改点的大小color参数修改点的颜色
```{r plot2}
#使用第17号形状
p1<-ggplot(data=boston_data, aes(x=lstat, y=medv)) + geom_point(shape=17)
#size参数修改点的大小color参数修改点的颜色
p2<-ggplot(data=boston_data, aes(x=lstat, y=medv)) + geom_point(size=3,color="red")
ggarrange(p1,p2,nrow = 1)
```
可将数据集的其它属性映射到散点图的颜色属性中
```{r plot4}
p3<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=factor(rad))) + geom_point()
p4<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=rad)) + geom_point()
ggarrange(p3,p4,nrow = 1)
```
ggplot2关于散点图的相关做法有很详细的介绍相关参考链接https://ggplot2.tidyverse.org/reference/geom_point.html
## 3.直方图
直方图是一种统计报告图,由一系列高度不等的纵向条纹或线段表示数据分布的情况。 一般用横轴表示数据类型,纵轴表示分布情况。
直方图可以很好的查看数据的分布情况,是常用的数据可视化展示图形。
我们对rad变量进行直方图分析
```{r plot6}
ggplot(data=boston_data, aes(x=rad)) + geom_histogram()
```
可以看到ggplot2可以自动对数据进行直方图的统计
我们给直方图填充颜色同时改变直方图类型color表示直方图的边框fill表示直方图中的填充颜色ggplot2支持RGB颜色表的配色方案linetype表示直方图线的类型
RGB颜色表可以参考http://www.mgzxzs.com/sytool/se.htm
```{r plot7}
p5<-ggplot(data=boston_data, aes(x=rad)) + geom_histogram(color="black",fill="#69b3a2")
p6<-ggplot(data=boston_data, aes(x=rad)) + geom_histogram(color="black",fill="#69b3a2",linetype="dashed")
ggarrange(p5,p6,nrow = 1)
```
ggplot2也支持在直方图上添加平均线和密度图
```{r plot8}
p7<-p5+geom_vline(aes(xintercept=mean(rad)),color="blue", linetype="dashed", size=1)
p8<-ggplot(data=boston_data, aes(x=rad)) + geom_histogram(color="black",fill="#69b3a2",aes(y=..density..))+
geom_density(alpha=.2, fill="#FF6666")
ggarrange(p7,p8,nrow = 1)
```
ggplot2关于直方图的相关做法有很详细的介绍相关参考链接https://ggplot2.tidyverse.org/reference/geom_histogram.html
## 4.柱状图
柱状图是一种常用的数据可视化图形,根据翻译的不同,柱状图又叫长条图、柱状统计图、条状图、棒形图
柱状图图用来比较两个或以上的价值(不同时间或者不同条件),只有一个变量,通常利用于较小的数据集分析。长条图亦可横向排列,或用多维方式表达。需要注意的是柱状图与直方图是不同的数据可视化方法,不要弄混淆了。
对h1n1数据集中填写人的受教育情况进行可视化展示,使用pylr包中的count对edcation进行计数统计
```{r plot9}
data<-count(h1n1_data['race'])
p<-ggplot(data,aes(x=race,y=freq))+geom_bar(stat="identity")
#也可以进行水平放置
p1 <- p + coord_flip()
ggarrange(p,p1)
```
可以看到左边的柱状图文字有点挡住了我们把文字旋转45°
```{r plot9a}
data<-count(h1n1_data['race'])
ggplot(data,aes(x=race,y=freq))+geom_bar(stat="identity")+theme(axis.text.x = element_text(angle = 45,hjust=1))
```
对柱状图的样式进行修改
```{r plot10}
# 更改条的宽度和颜色:
# 更改条的宽度
p2 <- ggplot(data, aes(x=race,y=freq)) +
geom_bar(stat="identity", width=0.5)+theme(axis.text.x = element_text(angle = 45,hjust=1))
# 改变颜色
p3 <- ggplot(data, aes(x=race,y=freq)) +
geom_bar(stat="identity", color="blue", fill="white")+theme(axis.text.x = element_text(angle = 45,hjust=1))
# 最小主题+蓝色填充颜色
p4 <- ggplot(data, aes(x=race,y=freq)) +
geom_bar(stat="identity", fill="steelblue")+
theme_minimal()+theme(axis.text.x = element_text(angle = 45,hjust=1))
# 选择要显示的项目
p5 <- p + scale_x_discrete(limits=c("White", "Black"))+theme(axis.text.x = element_text(angle = 45,hjust=1))
ggarrange(p2,p3,p4,p5)
```
对柱状图进行标签显示
```{r plot11}
p6 <- ggplot(data=data, aes(x=race,y=freq)) +
geom_bar(stat="identity", fill="steelblue")+
geom_text(aes(label=freq), vjust=-0.3, size=3.5)+
theme_minimal()+theme(axis.text.x = element_text(angle = 45,hjust=1))
# 条形内部标签
p7 <- ggplot(data=data, aes(x=race,y=freq)) +
geom_bar(stat="identity", fill="steelblue")+
geom_text(aes(label=freq), vjust=1.6, color="white", size=3.5)+
theme_minimal()+theme(axis.text.x = element_text(angle = 45,hjust=1))
ggarrange(p6,p7,nrow = 1)
```
如果觉得柱状图的顺序不是你想要的,可以对柱状图的顺序进行修改
```{r plot12}
data<-within(data,{
race<-factor(race,levels=c("White","Black","Hispanic","Other or Multiple"))
})
ggplot(data,aes(x=race,y=freq))+geom_bar(stat="identity", fill="steelblue")+theme(axis.text.x = element_text(angle = 45,hjust=1))
```
ggplot2关于柱状图的相关做法有很详细的介绍相关参考链接
https://ggplot2.tidyverse.org/reference/geom_bar.html
## 5.饼状图
饼状图作为常用的数据可视化图形之一,广泛的使用在各个领域,能够很清楚展示数据的所占的百分比。
ggplot2并没有类似于geom_pie()这样的函数实现饼图的绘制但ggplot2有一个理念就是通过极坐标变换绘制饼图
饼图在ggplot2中就是通过极坐标变换获得在绘制饼图之前需要绘制堆叠的条形图通过将条形图进行极坐标变换后就能实现饼图绘制了。
对h1n1问卷表中race数据进行数据展示
```{r plot13}
data<-count(h1n1_data['race'])
ggplot(data = data, aes(x ='', y = freq, fill = race)) + geom_bar(stat = 'identity')
```
堆叠的条形图绘制完后接下来就需要进行极坐标变换了ggplot2中coord_polar()函数可以非常方便的实现极坐标变换。
```{r plot14}
ggplot(data = data, aes(x ='', y = freq, fill = race)) + geom_bar(stat = 'identity')+coord_polar(theta = 'y')
```
看起来像饼图了,但是饼图周围还有多余的数字,如何清除呢?
这里的标签其实就是坐标轴的标签可以通过labs()函数将其清除。
```{r plot15}
ggplot(data = data, aes(x ='', y = freq, fill = race)) + geom_bar(stat = 'identity')+coord_polar(theta = 'y')+labs(x = '', y = '', title = '') + theme(axis.text = element_blank())
```
接下来就是显示各个所占的比例
第一种方法,将百分比直接显示在图例中,这种方式适合分类较多的情况。
```{r }
label_value <- paste('(', round(data$freq/sum(data$freq) * 100, 1), '%)', sep = '')
label_value
```
将计算的百分比和race匹配
```{r }
label <- paste(data$race, label_value, sep = '')
label
```
接下来就是将这些百分比标签放到图例中
```{r }
ggplot(data = data, aes(x ='', y = freq, fill = race)) + geom_bar(stat = 'identity')+coord_polar(theta = 'y')+labs(x = '', y = '', title = '') + theme(axis.text = element_blank())+scale_fill_discrete(labels = label)
```
看起来就很不错~
第二种方法,直接将百分比放到各自的饼区中。
首先是去掉饼图中的图例
```{r }
ggplot(data = data, aes(x ='', y = freq, fill = race)) + geom_bar(stat = 'identity')+coord_polar(theta = 'y')+labs(x = '', y = '', title = '') + theme(axis.text = element_blank())+theme(legend.position = "none")
```
将标签放置在饼图中
```{r }
ggplot(data = data, aes(x ='', y = freq, fill = race)) +
geom_bar(stat = 'identity',width = 1)+
coord_polar(theta = 'y')+labs(x = '', y = '', title = '') +
theme(axis.text = element_blank(),legend.position = "none") +
geom_text(aes(label = label), size=3, position = position_stack(vjust = 0.5))
```
## 6.折线图
折线图作为反映数据变化的趋势是常用的数据可视化图形之一在ggplot2中通过geom_line()这个函数进行绘制。
对波士顿房价中rad进行可视化展示使用pylr包中的count对edcation进行计数统计
```{r }
data<-count(boston_data["rad"])
data
```
把rad为24的数据去除掉
```{r }
data<-data[1:8,]
ggplot(data,aes(x=rad,y=freq))+geom_line()
```
有时候我们需要在折线图上显示对应x轴的点数据从而可以更加清晰的辨别原始数据,这特别适合数据比较稀疏的情况
```{r }
ggplot(data,aes(x=rad,y=freq))+geom_line()+geom_point(size=4)
```
我们调整横坐标的显示刻度
```{r }
ggplot(data,aes(x=rad,y=freq))+geom_line()+geom_point(size=4)+scale_x_continuous(breaks =c(1:8))
```
也可以修改线的类型和颜色
```{r }
ggplot(data,aes(x=rad,y=freq))+geom_line(linetype = "dashed",color="red")+geom_point(size=4)+scale_x_continuous(breaks =c(1:8))
```
ggplt2关于折线图的相关做法的参考链接
https://ggplot2.tidyverse.org/reference/geom_abline.html
## 7.ggplot2扩展包主题
R语言中的ggplot2包里面的风格固定在需要特殊的图形时需要更改甚至自定义设置主题。
ggplot2内置了8种风格的主题
|主题函数|效果|
|---|---|
|theme_bw()|网格白色主题|
|theme_classic()|经典主题|
|theme_dark()| 暗色主题,可用于对比|
|theme_gray()|默认主题|
|theme_light()|浅色坐标带网格|
|theme_linedraw()|黑色网格线|
|theme_minimal()|极简主题|
|theme_void()|空白主题|
我们来试一试不同的主题
```{r}
p<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=rad)) + geom_point()
p1<-p + theme_bw() + labs(title = "网格白色主题")+ theme(legend.position = "none")
p2<-p + theme_classic() + labs(title = "经典主题")+ theme(legend.position = "none")
p3<-p + theme_dark() + labs(title = "暗色主题")+ theme(legend.position = "none")
p4<-p + theme_gray() + labs(title = "默认主题")+ theme(legend.position = "none")
p5<-p + theme_light() + labs(title = "浅色坐标带网格")+ theme(legend.position = "none")
p6<-p + theme_linedraw() + labs(title = "黑色网格线")+ theme(legend.position = "none")
p7<-p + theme_minimal() + labs(title = "极简主题")+ theme(legend.position = "none")
p8<-p + theme_void() + labs(title = "空白主题")+ theme(legend.position = "none")
ggarrange(p1,p2,p3,p4,p5,p6,p7,p8,ncol= 4,nrow = 2,heights = 1.2)
```
除了ggplot2自带的主题外还有许多拓展主题包比如ggthemes、ggthemr
ggthemes在cran上发布因此推荐使用这个
ggthemr 色彩很好看,因此推荐这个
ggthemes相关链接https://github.com/jrnold/ggthemes
ggthemr相关链接https://github.com/Mikata-Project/ggthemr
因为ggthemr没有上cran因此需要通过github安装
```{r}
#devtools::install_github('Mikata-Project/ggthemr')
```
使用方法也是非常简单这里用我比较喜欢的greyscale主题方案
```{r}
library(ggthemr)
ggthemr('greyscale')
p3<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=factor(rad))) + geom_point()
p4<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=rad)) + geom_point()
ggarrange(p3,p4,nrow = 1)
```
试一试light这个主题配色非常的温柔
```{r}
library(ggthemr)
ggthemr('light')
p3<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=factor(rad))) + geom_point()
p4<-ggplot(data=boston_data, aes(x=lstat, y=medv,colour=rad)) + geom_point()
ggarrange(p3,p4,nrow = 1)
```
实战部分:
对提供的数据集我们可以试一试ggthemr中的不同主题同时对波士顿房价进行其它的数据可视化的探索。
ggplot2是一个非常经典的数据可视化R包内容非常丰富由于篇幅的原因没办法将ggplot2中的各种方法全部讲述因此选择了几个常见的图形进行相关的讲解以期达到抛砖引玉的效果。如果对ggplot2感兴趣的同学可以去官网进行更加详细的学习也非常期待大家的数据可视化作品~
**Task4 END.**
--- By: 牧小熊
> 华中农业大学研究生Datawhale成员, Datawhale优秀原创作者
>
> 知乎https://www.zhihu.com/people/muxiaoxiong
关于Datawhale Datawhale是一个专注于数据科学与AI领域的开源组织汇集了众多领域院校和知名企业的优秀学习者聚合了一群有开源精神和探索精神的团队成员。Datawhale 以“for the learner和学习者一起成长”为愿景鼓励真实地展现自我、开放包容、互信互助、敢于试错和勇于担当。同时 Datawhale 用开源的理念去探索开源内容、开源学习和开源方案,赋能人才培养,助力人才成长,建立起人与人,人与知识,人与企业和人与未来的联结。 本次数据挖掘路径学习专题知识将在天池分享详情可关注Datawhale
[![logo.png](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)

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---
title: |
| DataWhale 组队学习 R语言数据分析
| Task05 模型建立
author: "Jin Zhang"
date: "`r Sys.Date()`"
header-includes:
- \usepackage{ctex}
urlcolor: blue
output:
prettydoc::html_pretty:
theme: cayman
highlight: github
number_section: no
toc: no
knit: (function(inputFile, encoding) {
rmarkdown::render(inputFile, encoding = encoding,
output_dir = "output", output_format = "all") })
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE,warning=FALSE, message=FALSE,tidy=TRUE,collapse=FALSE)
```
![](./image/task05_structure.png){width=100%}
Task05共计3个知识点预计需学习2-3小时请安排好学习任务。
## 1 前言
为了帮助大家更好的使用R语言进行建模分析本章节将借助波士顿房价数据集来展示常见的模型。本章节学习的目的是帮助大家了解模型的适用范围以及如何建模不会对模型的底层原理进行深入的研究。并且迫于时间和精力有限本章节仅介绍部分模型的实现。
- 回归模型: 回归模型是一种有监督的、预测性的建模技术,它研究的是因变量和自变量之间的关系。
- 分类模型: 分类模型也是一种有监督的机器学习模型。与回归模型不同的是,其标签(因变量)通常是有限个数的定类变量。最常见的是二分类模型。
我们主要使用波士顿房价数据集来实现各种模型。因此我们使用2021作为种子值生成70%的数据作为训练集,其余数据作为测试集。下面展示来各个数据集的大小。
```{r }
# 导入BostonHousing数据
library(mlbench)
data(BostonHousing)
# 设置种子值,方便复现
set.seed(2021)
# 生成训练集的索引,用来划分训练集和测试集
train_index <- sample(dim(BostonHousing)[1],0.7*dim(BostonHousing)[1])
BostonHousingTrain <- BostonHousing[train_index,]
BostonHousingTest <- BostonHousing[-train_index,]
# 查看数据集的size
dim(BostonHousing)
dim(BostonHousingTrain)
dim(BostonHousingTest)
# 查看数据集包含的变量名称
names(BostonHousing)
```
## 2 回归模型
回归模型有很多主要有Linear Regression、Logistic Regression、Polynomial Regression、Stepwise Regression、Ridge Regression、Lasso Regression、ElasticNet等。
本部分主要介绍有Linear Regression、以及Stepwise Regression三种回归模型的实现。
### 2.1 Linear Regression
多元线性回归是一种最为基础的回归模型其使用多个自变量和一个因变量利用OLS完成模型训练。下面我们将使用`medv`作为因变量,剩余变量作为自变量构建模型。
多元线性回归模型使用`lm()`命令, 其中`medv~.`是回归公式,`data=BostonHousingTrain`是回归数据。对回归公式的构建进行一些补充,`~`左侧表示因变量,`~`右侧表示自变量,多个自变量使用`+`依次叠加。这里右侧使用了`.`,该符号的含义是除左侧变量外所有的变量。因此,`medv~.`等价于`medv~crim + zn + indus + chas + nox + rm + age + dis + rad + tax + ptratio + b + medv`。
```{r }
# 构建模型medv~.表示回归方程
lr_model <- lm(medv~.,data=BostonHousingTrain)
# summary输出模型汇总
summary(lr_model)
```
运用plot命令对模型进行诊断各图含义参考 https://www.cnblogs.com/lafengdatascientist/p/5554167.html
```{r }
plot(lr_model)
```
`predict`命令能够基于已经训练好的模型进行预测。
```{r }
# 根据模型对新数据进行预测
BostonHousingTest$lr_pred <- predict(lr_model,newdata = BostonHousingTest)
```
### 2.2 Stepwise Regression
利用逐步回归分析可以对模型中的变量进行优化。R语言中的`step()`命令,是以AIC信息统计量为准则通过选择最小的AIC信息统计量来达到提出或添加变量的目的。
对于逐步回归,一般有前向、后向、双向等逐步方式。本部分将基于已经实现的`lr_model`进行双向逐步回归。前向和后向回归只需要更改`step()`命令行中的`direstion`参数即可。具体内容参照 https://blog.csdn.net/qq_38204302/article/details/86567356
```{r }
# both逐步回归
step_model <- step(lr_model,direction="both")
summary(step_model)
```
对于分类模型还有较为常用的Lasso Regression 和 Ridge Regression我们将会在进阶教程中来更加具体的讲解模型知识。
## 3 分类模型
在进行分类模型前,我们需要构建分类标签。我们使用`medv`的中位数进行划分其中1表示高房价0表示低房价。通过这样的转化将原本的数值型变量转化为二元标签。并使用相同的种子值划分测试集和训练集。
```{r }
# 将连续变量转化成二分类变量
BostonHousing$medv <- as.factor(ifelse(BostonHousing$medv > median(BostonHousing$medv),1,0))
# 查看两种变量类别的数量
summary(BostonHousing$medv)
# 使用相同的种子值,复现训练集合测试集的划分
set.seed(2021)
train_index <- sample(dim(BostonHousing)[1],0.7*dim(BostonHousing)[1])
BostonHousingTrain <- BostonHousing[train_index,]
BostonHousingTest <- BostonHousing[-train_index,]
```
同时引入两个计算函数用来计算AUC指标值。
```{r }
# 引入auc计算函数
library('ROCR')
calcAUC <-function(predcol,outcol) {
perf <-performance(prediction(predcol,outcol==1),'auc')
as.numeric(perf@y.values)
}
```
### 3.1 Logistics Regression
逻辑回归是一种广义的线性回归分析模型利用sigmode将线性回归结果转化成概率的形式。下面展示了利用`glm()`构建逻辑回归的过程。通过计算训练集上的auc取值为0.9554211测试集上的auc取值为0.9506969,说明模型效果整体不错。
```{r }
# 逻辑回归模型构建
lr_model <-glm(medv~., data=BostonHousingTrain, family=binomial(link="logit"))
summary(lr_model)
# 分别对训练集和测试集进行预测
lr_pred_train <- predict(lr_model, newdata=BostonHousingTrain, type="response")
lr_pred_test <- predict(lr_model, newdata=BostonHousingTest, type="response")
# 计算训练集和测试集的auc
calcAUC(lr_pred_train,BostonHousingTrain$medv)
calcAUC(lr_pred_test,BostonHousingTest$medv)
```
### 3.2 KNN
KNN模型是一种简单易懂、可以用于分类和回归的模型。其中 K 表示在新样本点附近(距离)选取 K 个样本数据,通过在 K 个样本进行投票来判断新增样本的类型。
KNN模型较难的一点是确定超参数K目前有一些指标和经验方法帮助确定最优K的取值。这部分内容会在后续进行讲解这里使用k=25进行建模。KNN模型在测试集上的auc值为0.8686411,相比于逻辑回归效果较差。
```{r }
# 导入knn模型的包
library(kknn)
# 构建knn模型
knn <- kknn(medv~., BostonHousingTrain, BostonHousingTest,k = 25)
# 预测并计算测试集上的auc取值
knn_pred_test <- predict(knn, newdata=BostonHousingTest)
calcAUC(as.numeric(knn_pred_test),BostonHousingTest$medv)
```
### 3.3 Decision Tree
决策树是一种基于树模型进行划分的分类模型通过一系列if then决策规则的集合将特征空间划分成有限个不相交的子区域对于落在相同子区域的样本决策树模型给出相同的预测值。下面构建了决策树的分类模型
```{r }
# 导入包
library(tree)
# 构建决策树模型函数medv~.是决策树公式,用来表明变量。
# summary输出模型汇总信息
dt_model <- tree(medv~., BostonHousingTrain)
summary(dt_model)
# plot可以对树模型进行绘制但可能会出现书分支过多的情况。
plot(dt_model)
text(dt_model)
```
在构建决策树模型的基础上分别对训练集和测试集进行预测并计算auc取值。该模型在训练集上的auc取值为0.9281874在测试集上的auc取值为0.8789199。训练集和测试集间存在抖动,说明该模型可能出现过拟合。我们需要引入剪枝的操作来降低模型的过拟合,这部分供同学们自学。
```{r }
# 预测
dt_pred_train <- predict(dt_model, newdata=BostonHousingTrain, type="class")
dt_pred_test <- predict(dt_model, newdata=BostonHousingTest, type="class")
# 计算auc取值
calcAUC(as.numeric(dt_pred_train),BostonHousingTrain$medv)
calcAUC(as.numeric(dt_pred_test),BostonHousingTest$medv)
```
### 3.4 Random Forest
随机森林是一个包含多个决策树的分类器,可以用于分类和回归问题。在解决分类问题是,其输出的类别是由个别树输出的类别的众数而定。相比于单树模型,随机森林具有更好地泛化能力。
使用`randomForest()`构建模型的过程中,可以通过`ntree`设定随机森林中包含的决策树数量。由于随机森林是对样本和变量的随机,因此可以通过`important`展示变量的重要性排序。通过模型预测随机森林模型在训练集上的auc为0.9615975在测试集上的auc为0.9247387。
```{r }
# 导入随机森林包
library(randomForest)
# 随机森林模型
rf_model <- randomForest(medv~., BostonHousingTrain,ntree=100,nodesize=10,importance=T)
# 展示模型变量的重要性
importance(rf_model)
# 预测
rf_pred_train <- predict(rf_model, newdata=BostonHousingTrain, type="class")
rf_pred_test <- predict(rf_model, newdata=BostonHousingTest, type="class")
# 计算auc取值
calcAUC(as.numeric(rf_pred_train),BostonHousingTrain$medv)
calcAUC(as.numeric(rf_pred_test),BostonHousingTest$medv)
```
## 思考与练习
本章节仅对模型进行简单介绍,更多详细、复杂的模型将在后面的进阶课程中展开。
学习完本章节希望你能够尝试一些模型调优工作。如决策树剪枝如尝试搜索KNN模型中最佳K取值等。
**Task5 END.**
--- By: 张晋
> Datawhale成员, 数据科学爱好者
关于Datawhale Datawhale是一个专注于数据科学与AI领域的开源组织汇集了众多领域院校和知名企业的优秀学习者聚合了一群有开源精神和探索精神的团队成员。Datawhale 以“for the learner和学习者一起成长”为愿景鼓励真实地展现自我、开放包容、互信互助、敢于试错和勇于担当。同时 Datawhale 用开源的理念去探索开源内容、开源学习和开源方案,赋能人才培养,助力人才成长,建立起人与人,人与知识,人与企业和人与未来的联结。 本次数据挖掘路径学习专题知识将在天池分享详情可关注Datawhale
[![logo.png](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)

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"357",8.98296,0,18.1,"1",0.77,6.212,97.4,2.1222,24,666,20.2,377.73,17.6,17.8
"358",3.8497,0,18.1,"1",0.77,6.395,91,2.5052,24,666,20.2,391.34,13.27,21.7
"359",5.20177,0,18.1,"1",0.77,6.127,83.4,2.7227,24,666,20.2,395.43,11.48,22.7
"360",4.26131,0,18.1,"0",0.77,6.112,81.3,2.5091,24,666,20.2,390.74,12.67,22.6
"361",4.54192,0,18.1,"0",0.77,6.398,88,2.5182,24,666,20.2,374.56,7.79,25
"362",3.83684,0,18.1,"0",0.77,6.251,91.1,2.2955,24,666,20.2,350.65,14.19,19.9
"363",3.67822,0,18.1,"0",0.77,5.362,96.2,2.1036,24,666,20.2,380.79,10.19,20.8
"364",4.22239,0,18.1,"1",0.77,5.803,89,1.9047,24,666,20.2,353.04,14.64,16.8
"365",3.47428,0,18.1,"1",0.718,8.78,82.9,1.9047,24,666,20.2,354.55,5.29,21.9
"366",4.55587,0,18.1,"0",0.718,3.561,87.9,1.6132,24,666,20.2,354.7,7.12,27.5
"367",3.69695,0,18.1,"0",0.718,4.963,91.4,1.7523,24,666,20.2,316.03,14,21.9
"368",13.5222,0,18.1,"0",0.631,3.863,100,1.5106,24,666,20.2,131.42,13.33,23.1
"369",4.89822,0,18.1,"0",0.631,4.97,100,1.3325,24,666,20.2,375.52,3.26,50
"370",5.66998,0,18.1,"1",0.631,6.683,96.8,1.3567,24,666,20.2,375.33,3.73,50
"371",6.53876,0,18.1,"1",0.631,7.016,97.5,1.2024,24,666,20.2,392.05,2.96,50
"372",9.2323,0,18.1,"0",0.631,6.216,100,1.1691,24,666,20.2,366.15,9.53,50
"373",8.26725,0,18.1,"1",0.668,5.875,89.6,1.1296,24,666,20.2,347.88,8.88,50
"374",11.1081,0,18.1,"0",0.668,4.906,100,1.1742,24,666,20.2,396.9,34.77,13.8
"375",18.4982,0,18.1,"0",0.668,4.138,100,1.137,24,666,20.2,396.9,37.97,13.8
"376",19.6091,0,18.1,"0",0.671,7.313,97.9,1.3163,24,666,20.2,396.9,13.44,15
"377",15.288,0,18.1,"0",0.671,6.649,93.3,1.3449,24,666,20.2,363.02,23.24,13.9
"378",9.82349,0,18.1,"0",0.671,6.794,98.8,1.358,24,666,20.2,396.9,21.24,13.3
"379",23.6482,0,18.1,"0",0.671,6.38,96.2,1.3861,24,666,20.2,396.9,23.69,13.1
"380",17.8667,0,18.1,"0",0.671,6.223,100,1.3861,24,666,20.2,393.74,21.78,10.2
"381",88.9762,0,18.1,"0",0.671,6.968,91.9,1.4165,24,666,20.2,396.9,17.21,10.4
"382",15.8744,0,18.1,"0",0.671,6.545,99.1,1.5192,24,666,20.2,396.9,21.08,10.9
"383",9.18702,0,18.1,"0",0.7,5.536,100,1.5804,24,666,20.2,396.9,23.6,11.3
"384",7.99248,0,18.1,"0",0.7,5.52,100,1.5331,24,666,20.2,396.9,24.56,12.3
"385",20.0849,0,18.1,"0",0.7,4.368,91.2,1.4395,24,666,20.2,285.83,30.63,8.8
"386",16.8118,0,18.1,"0",0.7,5.277,98.1,1.4261,24,666,20.2,396.9,30.81,7.2
"387",24.3938,0,18.1,"0",0.7,4.652,100,1.4672,24,666,20.2,396.9,28.28,10.5
"388",22.5971,0,18.1,"0",0.7,5,89.5,1.5184,24,666,20.2,396.9,31.99,7.4
"389",14.3337,0,18.1,"0",0.7,4.88,100,1.5895,24,666,20.2,372.92,30.62,10.2
"390",8.15174,0,18.1,"0",0.7,5.39,98.9,1.7281,24,666,20.2,396.9,20.85,11.5
"391",6.96215,0,18.1,"0",0.7,5.713,97,1.9265,24,666,20.2,394.43,17.11,15.1
"392",5.29305,0,18.1,"0",0.7,6.051,82.5,2.1678,24,666,20.2,378.38,18.76,23.2
"393",11.5779,0,18.1,"0",0.7,5.036,97,1.77,24,666,20.2,396.9,25.68,9.7
"394",8.64476,0,18.1,"0",0.693,6.193,92.6,1.7912,24,666,20.2,396.9,15.17,13.8
"395",13.3598,0,18.1,"0",0.693,5.887,94.7,1.7821,24,666,20.2,396.9,16.35,12.7
"396",8.71675,0,18.1,"0",0.693,6.471,98.8,1.7257,24,666,20.2,391.98,17.12,13.1
"397",5.87205,0,18.1,"0",0.693,6.405,96,1.6768,24,666,20.2,396.9,19.37,12.5
"398",7.67202,0,18.1,"0",0.693,5.747,98.9,1.6334,24,666,20.2,393.1,19.92,8.5
"399",38.3518,0,18.1,"0",0.693,5.453,100,1.4896,24,666,20.2,396.9,30.59,5
"400",9.91655,0,18.1,"0",0.693,5.852,77.8,1.5004,24,666,20.2,338.16,29.97,6.3
"401",25.0461,0,18.1,"0",0.693,5.987,100,1.5888,24,666,20.2,396.9,26.77,5.6
"402",14.2362,0,18.1,"0",0.693,6.343,100,1.5741,24,666,20.2,396.9,20.32,7.2
"403",9.59571,0,18.1,"0",0.693,6.404,100,1.639,24,666,20.2,376.11,20.31,12.1
"404",24.8017,0,18.1,"0",0.693,5.349,96,1.7028,24,666,20.2,396.9,19.77,8.3
"405",41.5292,0,18.1,"0",0.693,5.531,85.4,1.6074,24,666,20.2,329.46,27.38,8.5
"406",67.9208,0,18.1,"0",0.693,5.683,100,1.4254,24,666,20.2,384.97,22.98,5
"407",20.7162,0,18.1,"0",0.659,4.138,100,1.1781,24,666,20.2,370.22,23.34,11.9
"408",11.9511,0,18.1,"0",0.659,5.608,100,1.2852,24,666,20.2,332.09,12.13,27.9
"409",7.40389,0,18.1,"0",0.597,5.617,97.9,1.4547,24,666,20.2,314.64,26.4,17.2
"410",14.4383,0,18.1,"0",0.597,6.852,100,1.4655,24,666,20.2,179.36,19.78,27.5
"411",51.1358,0,18.1,"0",0.597,5.757,100,1.413,24,666,20.2,2.6,10.11,15
"412",14.0507,0,18.1,"0",0.597,6.657,100,1.5275,24,666,20.2,35.05,21.22,17.2
"413",18.811,0,18.1,"0",0.597,4.628,100,1.5539,24,666,20.2,28.79,34.37,17.9
"414",28.6558,0,18.1,"0",0.597,5.155,100,1.5894,24,666,20.2,210.97,20.08,16.3
"415",45.7461,0,18.1,"0",0.693,4.519,100,1.6582,24,666,20.2,88.27,36.98,7
"416",18.0846,0,18.1,"0",0.679,6.434,100,1.8347,24,666,20.2,27.25,29.05,7.2
"417",10.8342,0,18.1,"0",0.679,6.782,90.8,1.8195,24,666,20.2,21.57,25.79,7.5
"418",25.9406,0,18.1,"0",0.679,5.304,89.1,1.6475,24,666,20.2,127.36,26.64,10.4
"419",73.5341,0,18.1,"0",0.679,5.957,100,1.8026,24,666,20.2,16.45,20.62,8.8
"420",11.8123,0,18.1,"0",0.718,6.824,76.5,1.794,24,666,20.2,48.45,22.74,8.4
"421",11.0874,0,18.1,"0",0.718,6.411,100,1.8589,24,666,20.2,318.75,15.02,16.7
"422",7.02259,0,18.1,"0",0.718,6.006,95.3,1.8746,24,666,20.2,319.98,15.7,14.2
"423",12.0482,0,18.1,"0",0.614,5.648,87.6,1.9512,24,666,20.2,291.55,14.1,20.8
"424",7.05042,0,18.1,"0",0.614,6.103,85.1,2.0218,24,666,20.2,2.52,23.29,13.4
"425",8.79212,0,18.1,"0",0.584,5.565,70.6,2.0635,24,666,20.2,3.65,17.16,11.7
"426",15.8603,0,18.1,"0",0.679,5.896,95.4,1.9096,24,666,20.2,7.68,24.39,8.3
"427",12.2472,0,18.1,"0",0.584,5.837,59.7,1.9976,24,666,20.2,24.65,15.69,10.2
"428",37.6619,0,18.1,"0",0.679,6.202,78.7,1.8629,24,666,20.2,18.82,14.52,10.9
"429",7.36711,0,18.1,"0",0.679,6.193,78.1,1.9356,24,666,20.2,96.73,21.52,11
"430",9.33889,0,18.1,"0",0.679,6.38,95.6,1.9682,24,666,20.2,60.72,24.08,9.5
"431",8.49213,0,18.1,"0",0.584,6.348,86.1,2.0527,24,666,20.2,83.45,17.64,14.5
"432",10.0623,0,18.1,"0",0.584,6.833,94.3,2.0882,24,666,20.2,81.33,19.69,14.1
"433",6.44405,0,18.1,"0",0.584,6.425,74.8,2.2004,24,666,20.2,97.95,12.03,16.1
"434",5.58107,0,18.1,"0",0.713,6.436,87.9,2.3158,24,666,20.2,100.19,16.22,14.3
"435",13.9134,0,18.1,"0",0.713,6.208,95,2.2222,24,666,20.2,100.63,15.17,11.7
"436",11.1604,0,18.1,"0",0.74,6.629,94.6,2.1247,24,666,20.2,109.85,23.27,13.4
"437",14.4208,0,18.1,"0",0.74,6.461,93.3,2.0026,24,666,20.2,27.49,18.05,9.6
"438",15.1772,0,18.1,"0",0.74,6.152,100,1.9142,24,666,20.2,9.32,26.45,8.7
"439",13.6781,0,18.1,"0",0.74,5.935,87.9,1.8206,24,666,20.2,68.95,34.02,8.4
"440",9.39063,0,18.1,"0",0.74,5.627,93.9,1.8172,24,666,20.2,396.9,22.88,12.8
"441",22.0511,0,18.1,"0",0.74,5.818,92.4,1.8662,24,666,20.2,391.45,22.11,10.5
"442",9.72418,0,18.1,"0",0.74,6.406,97.2,2.0651,24,666,20.2,385.96,19.52,17.1
"443",5.66637,0,18.1,"0",0.74,6.219,100,2.0048,24,666,20.2,395.69,16.59,18.4
"444",9.96654,0,18.1,"0",0.74,6.485,100,1.9784,24,666,20.2,386.73,18.85,15.4
"445",12.8023,0,18.1,"0",0.74,5.854,96.6,1.8956,24,666,20.2,240.52,23.79,10.8
"446",10.6718,0,18.1,"0",0.74,6.459,94.8,1.9879,24,666,20.2,43.06,23.98,11.8
"447",6.28807,0,18.1,"0",0.74,6.341,96.4,2.072,24,666,20.2,318.01,17.79,14.9
"448",9.92485,0,18.1,"0",0.74,6.251,96.6,2.198,24,666,20.2,388.52,16.44,12.6
"449",9.32909,0,18.1,"0",0.713,6.185,98.7,2.2616,24,666,20.2,396.9,18.13,14.1
"450",7.52601,0,18.1,"0",0.713,6.417,98.3,2.185,24,666,20.2,304.21,19.31,13
"451",6.71772,0,18.1,"0",0.713,6.749,92.6,2.3236,24,666,20.2,0.32,17.44,13.4
"452",5.44114,0,18.1,"0",0.713,6.655,98.2,2.3552,24,666,20.2,355.29,17.73,15.2
"453",5.09017,0,18.1,"0",0.713,6.297,91.8,2.3682,24,666,20.2,385.09,17.27,16.1
"454",8.24809,0,18.1,"0",0.713,7.393,99.3,2.4527,24,666,20.2,375.87,16.74,17.8
"455",9.51363,0,18.1,"0",0.713,6.728,94.1,2.4961,24,666,20.2,6.68,18.71,14.9
"456",4.75237,0,18.1,"0",0.713,6.525,86.5,2.4358,24,666,20.2,50.92,18.13,14.1
"457",4.66883,0,18.1,"0",0.713,5.976,87.9,2.5806,24,666,20.2,10.48,19.01,12.7
"458",8.20058,0,18.1,"0",0.713,5.936,80.3,2.7792,24,666,20.2,3.5,16.94,13.5
"459",7.75223,0,18.1,"0",0.713,6.301,83.7,2.7831,24,666,20.2,272.21,16.23,14.9
"460",6.80117,0,18.1,"0",0.713,6.081,84.4,2.7175,24,666,20.2,396.9,14.7,20
"461",4.81213,0,18.1,"0",0.713,6.701,90,2.5975,24,666,20.2,255.23,16.42,16.4
"462",3.69311,0,18.1,"0",0.713,6.376,88.4,2.5671,24,666,20.2,391.43,14.65,17.7
"463",6.65492,0,18.1,"0",0.713,6.317,83,2.7344,24,666,20.2,396.9,13.99,19.5
"464",5.82115,0,18.1,"0",0.713,6.513,89.9,2.8016,24,666,20.2,393.82,10.29,20.2
"465",7.83932,0,18.1,"0",0.655,6.209,65.4,2.9634,24,666,20.2,396.9,13.22,21.4
"466",3.1636,0,18.1,"0",0.655,5.759,48.2,3.0665,24,666,20.2,334.4,14.13,19.9
"467",3.77498,0,18.1,"0",0.655,5.952,84.7,2.8715,24,666,20.2,22.01,17.15,19
"468",4.42228,0,18.1,"0",0.584,6.003,94.5,2.5403,24,666,20.2,331.29,21.32,19.1
"469",15.5757,0,18.1,"0",0.58,5.926,71,2.9084,24,666,20.2,368.74,18.13,19.1
"470",13.0751,0,18.1,"0",0.58,5.713,56.7,2.8237,24,666,20.2,396.9,14.76,20.1
"471",4.34879,0,18.1,"0",0.58,6.167,84,3.0334,24,666,20.2,396.9,16.29,19.9
"472",4.03841,0,18.1,"0",0.532,6.229,90.7,3.0993,24,666,20.2,395.33,12.87,19.6
"473",3.56868,0,18.1,"0",0.58,6.437,75,2.8965,24,666,20.2,393.37,14.36,23.2
"474",4.64689,0,18.1,"0",0.614,6.98,67.6,2.5329,24,666,20.2,374.68,11.66,29.8
"475",8.05579,0,18.1,"0",0.584,5.427,95.4,2.4298,24,666,20.2,352.58,18.14,13.8
"476",6.39312,0,18.1,"0",0.584,6.162,97.4,2.206,24,666,20.2,302.76,24.1,13.3
"477",4.87141,0,18.1,"0",0.614,6.484,93.6,2.3053,24,666,20.2,396.21,18.68,16.7
"478",15.0234,0,18.1,"0",0.614,5.304,97.3,2.1007,24,666,20.2,349.48,24.91,12
"479",10.233,0,18.1,"0",0.614,6.185,96.7,2.1705,24,666,20.2,379.7,18.03,14.6
"480",14.3337,0,18.1,"0",0.614,6.229,88,1.9512,24,666,20.2,383.32,13.11,21.4
"481",5.82401,0,18.1,"0",0.532,6.242,64.7,3.4242,24,666,20.2,396.9,10.74,23
"482",5.70818,0,18.1,"0",0.532,6.75,74.9,3.3317,24,666,20.2,393.07,7.74,23.7
"483",5.73116,0,18.1,"0",0.532,7.061,77,3.4106,24,666,20.2,395.28,7.01,25
"484",2.81838,0,18.1,"0",0.532,5.762,40.3,4.0983,24,666,20.2,392.92,10.42,21.8
"485",2.37857,0,18.1,"0",0.583,5.871,41.9,3.724,24,666,20.2,370.73,13.34,20.6
"486",3.67367,0,18.1,"0",0.583,6.312,51.9,3.9917,24,666,20.2,388.62,10.58,21.2
"487",5.69175,0,18.1,"0",0.583,6.114,79.8,3.5459,24,666,20.2,392.68,14.98,19.1
"488",4.83567,0,18.1,"0",0.583,5.905,53.2,3.1523,24,666,20.2,388.22,11.45,20.6
"489",0.15086,0,27.74,"0",0.609,5.454,92.7,1.8209,4,711,20.1,395.09,18.06,15.2
"490",0.18337,0,27.74,"0",0.609,5.414,98.3,1.7554,4,711,20.1,344.05,23.97,7
"491",0.20746,0,27.74,"0",0.609,5.093,98,1.8226,4,711,20.1,318.43,29.68,8.1
"492",0.10574,0,27.74,"0",0.609,5.983,98.8,1.8681,4,711,20.1,390.11,18.07,13.6
"493",0.11132,0,27.74,"0",0.609,5.983,83.5,2.1099,4,711,20.1,396.9,13.35,20.1
"494",0.17331,0,9.69,"0",0.585,5.707,54,2.3817,6,391,19.2,396.9,12.01,21.8
"495",0.27957,0,9.69,"0",0.585,5.926,42.6,2.3817,6,391,19.2,396.9,13.59,24.5
"496",0.17899,0,9.69,"0",0.585,5.67,28.8,2.7986,6,391,19.2,393.29,17.6,23.1
"497",0.2896,0,9.69,"0",0.585,5.39,72.9,2.7986,6,391,19.2,396.9,21.14,19.7
"498",0.26838,0,9.69,"0",0.585,5.794,70.6,2.8927,6,391,19.2,396.9,14.1,18.3
"499",0.23912,0,9.69,"0",0.585,6.019,65.3,2.4091,6,391,19.2,396.9,12.92,21.2
"500",0.17783,0,9.69,"0",0.585,5.569,73.5,2.3999,6,391,19.2,395.77,15.1,17.5
"501",0.22438,0,9.69,"0",0.585,6.027,79.7,2.4982,6,391,19.2,396.9,14.33,16.8
"502",0.06263,0,11.93,"0",0.573,6.593,69.1,2.4786,1,273,21,391.99,9.67,22.4
"503",0.04527,0,11.93,"0",0.573,6.12,76.7,2.2875,1,273,21,396.9,9.08,20.6
"504",0.06076,0,11.93,"0",0.573,6.976,91,2.1675,1,273,21,396.9,5.64,23.9
"505",0.10959,0,11.93,"0",0.573,6.794,89.3,2.3889,1,273,21,393.45,6.48,22
"506",0.04741,0,11.93,"0",0.573,6.03,80.8,2.505,1,273,21,396.9,7.88,11.9
1 crim zn indus chas nox rm age dis rad tax ptratio b lstat medv
2 1 0.00632 18 2.31 0 0.538 6.575 65.2 4.09 1 296 15.3 396.9 4.98 24
3 2 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.9 9.14 21.6
4 3 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83 4.03 34.7
5 4 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 394.63 2.94 33.4
6 5 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 396.9 5.33 36.2
7 6 0.02985 0 2.18 0 0.458 6.43 58.7 6.0622 3 222 18.7 394.12 5.21 28.7
8 7 0.08829 12.5 7.87 0 0.524 6.012 66.6 5.5605 5 311 15.2 395.6 12.43 22.9
9 8 0.14455 12.5 7.87 0 0.524 6.172 96.1 5.9505 5 311 15.2 396.9 19.15 27.1
10 9 0.21124 12.5 7.87 0 0.524 5.631 100 6.0821 5 311 15.2 386.63 29.93 16.5
11 10 0.17004 12.5 7.87 0 0.524 6.004 85.9 6.5921 5 311 15.2 386.71 17.1 18.9
12 11 0.22489 12.5 7.87 0 0.524 6.377 94.3 6.3467 5 311 15.2 392.52 20.45 15
13 12 0.11747 12.5 7.87 0 0.524 6.009 82.9 6.2267 5 311 15.2 396.9 13.27 18.9
14 13 0.09378 12.5 7.87 0 0.524 5.889 39 5.4509 5 311 15.2 390.5 15.71 21.7
15 14 0.62976 0 8.14 0 0.538 5.949 61.8 4.7075 4 307 21 396.9 8.26 20.4
16 15 0.63796 0 8.14 0 0.538 6.096 84.5 4.4619 4 307 21 380.02 10.26 18.2
17 16 0.62739 0 8.14 0 0.538 5.834 56.5 4.4986 4 307 21 395.62 8.47 19.9
18 17 1.05393 0 8.14 0 0.538 5.935 29.3 4.4986 4 307 21 386.85 6.58 23.1
19 18 0.7842 0 8.14 0 0.538 5.99 81.7 4.2579 4 307 21 386.75 14.67 17.5
20 19 0.80271 0 8.14 0 0.538 5.456 36.6 3.7965 4 307 21 288.99 11.69 20.2
21 20 0.7258 0 8.14 0 0.538 5.727 69.5 3.7965 4 307 21 390.95 11.28 18.2
22 21 1.25179 0 8.14 0 0.538 5.57 98.1 3.7979 4 307 21 376.57 21.02 13.6
23 22 0.85204 0 8.14 0 0.538 5.965 89.2 4.0123 4 307 21 392.53 13.83 19.6
24 23 1.23247 0 8.14 0 0.538 6.142 91.7 3.9769 4 307 21 396.9 18.72 15.2
25 24 0.98843 0 8.14 0 0.538 5.813 100 4.0952 4 307 21 394.54 19.88 14.5
26 25 0.75026 0 8.14 0 0.538 5.924 94.1 4.3996 4 307 21 394.33 16.3 15.6
27 26 0.84054 0 8.14 0 0.538 5.599 85.7 4.4546 4 307 21 303.42 16.51 13.9
28 27 0.67191 0 8.14 0 0.538 5.813 90.3 4.682 4 307 21 376.88 14.81 16.6
29 28 0.95577 0 8.14 0 0.538 6.047 88.8 4.4534 4 307 21 306.38 17.28 14.8
30 29 0.77299 0 8.14 0 0.538 6.495 94.4 4.4547 4 307 21 387.94 12.8 18.4
31 30 1.00245 0 8.14 0 0.538 6.674 87.3 4.239 4 307 21 380.23 11.98 21
32 31 1.13081 0 8.14 0 0.538 5.713 94.1 4.233 4 307 21 360.17 22.6 12.7
33 32 1.35472 0 8.14 0 0.538 6.072 100 4.175 4 307 21 376.73 13.04 14.5
34 33 1.38799 0 8.14 0 0.538 5.95 82 3.99 4 307 21 232.6 27.71 13.2
35 34 1.15172 0 8.14 0 0.538 5.701 95 3.7872 4 307 21 358.77 18.35 13.1
36 35 1.61282 0 8.14 0 0.538 6.096 96.9 3.7598 4 307 21 248.31 20.34 13.5
37 36 0.06417 0 5.96 0 0.499 5.933 68.2 3.3603 5 279 19.2 396.9 9.68 18.9
38 37 0.09744 0 5.96 0 0.499 5.841 61.4 3.3779 5 279 19.2 377.56 11.41 20
39 38 0.08014 0 5.96 0 0.499 5.85 41.5 3.9342 5 279 19.2 396.9 8.77 21
40 39 0.17505 0 5.96 0 0.499 5.966 30.2 3.8473 5 279 19.2 393.43 10.13 24.7
41 40 0.02763 75 2.95 0 0.428 6.595 21.8 5.4011 3 252 18.3 395.63 4.32 30.8
42 41 0.03359 75 2.95 0 0.428 7.024 15.8 5.4011 3 252 18.3 395.62 1.98 34.9
43 42 0.12744 0 6.91 0 0.448 6.77 2.9 5.7209 3 233 17.9 385.41 4.84 26.6
44 43 0.1415 0 6.91 0 0.448 6.169 6.6 5.7209 3 233 17.9 383.37 5.81 25.3
45 44 0.15936 0 6.91 0 0.448 6.211 6.5 5.7209 3 233 17.9 394.46 7.44 24.7
46 45 0.12269 0 6.91 0 0.448 6.069 40 5.7209 3 233 17.9 389.39 9.55 21.2
47 46 0.17142 0 6.91 0 0.448 5.682 33.8 5.1004 3 233 17.9 396.9 10.21 19.3
48 47 0.18836 0 6.91 0 0.448 5.786 33.3 5.1004 3 233 17.9 396.9 14.15 20
49 48 0.22927 0 6.91 0 0.448 6.03 85.5 5.6894 3 233 17.9 392.74 18.8 16.6
50 49 0.25387 0 6.91 0 0.448 5.399 95.3 5.87 3 233 17.9 396.9 30.81 14.4
51 50 0.21977 0 6.91 0 0.448 5.602 62 6.0877 3 233 17.9 396.9 16.2 19.4
52 51 0.08873 21 5.64 0 0.439 5.963 45.7 6.8147 4 243 16.8 395.56 13.45 19.7
53 52 0.04337 21 5.64 0 0.439 6.115 63 6.8147 4 243 16.8 393.97 9.43 20.5
54 53 0.0536 21 5.64 0 0.439 6.511 21.1 6.8147 4 243 16.8 396.9 5.28 25
55 54 0.04981 21 5.64 0 0.439 5.998 21.4 6.8147 4 243 16.8 396.9 8.43 23.4
56 55 0.0136 75 4 0 0.41 5.888 47.6 7.3197 3 469 21.1 396.9 14.8 18.9
57 56 0.01311 90 1.22 0 0.403 7.249 21.9 8.6966 5 226 17.9 395.93 4.81 35.4
58 57 0.02055 85 0.74 0 0.41 6.383 35.7 9.1876 2 313 17.3 396.9 5.77 24.7
59 58 0.01432 100 1.32 0 0.411 6.816 40.5 8.3248 5 256 15.1 392.9 3.95 31.6
60 59 0.15445 25 5.13 0 0.453 6.145 29.2 7.8148 8 284 19.7 390.68 6.86 23.3
61 60 0.10328 25 5.13 0 0.453 5.927 47.2 6.932 8 284 19.7 396.9 9.22 19.6
62 61 0.14932 25 5.13 0 0.453 5.741 66.2 7.2254 8 284 19.7 395.11 13.15 18.7
63 62 0.17171 25 5.13 0 0.453 5.966 93.4 6.8185 8 284 19.7 378.08 14.44 16
64 63 0.11027 25 5.13 0 0.453 6.456 67.8 7.2255 8 284 19.7 396.9 6.73 22.2
65 64 0.1265 25 5.13 0 0.453 6.762 43.4 7.9809 8 284 19.7 395.58 9.5 25
66 65 0.01951 17.5 1.38 0 0.4161 7.104 59.5 9.2229 3 216 18.6 393.24 8.05 33
67 66 0.03584 80 3.37 0 0.398 6.29 17.8 6.6115 4 337 16.1 396.9 4.67 23.5
68 67 0.04379 80 3.37 0 0.398 5.787 31.1 6.6115 4 337 16.1 396.9 10.24 19.4
69 68 0.05789 12.5 6.07 0 0.409 5.878 21.4 6.498 4 345 18.9 396.21 8.1 22
70 69 0.13554 12.5 6.07 0 0.409 5.594 36.8 6.498 4 345 18.9 396.9 13.09 17.4
71 70 0.12816 12.5 6.07 0 0.409 5.885 33 6.498 4 345 18.9 396.9 8.79 20.9
72 71 0.08826 0 10.81 0 0.413 6.417 6.6 5.2873 4 305 19.2 383.73 6.72 24.2
73 72 0.15876 0 10.81 0 0.413 5.961 17.5 5.2873 4 305 19.2 376.94 9.88 21.7
74 73 0.09164 0 10.81 0 0.413 6.065 7.8 5.2873 4 305 19.2 390.91 5.52 22.8
75 74 0.19539 0 10.81 0 0.413 6.245 6.2 5.2873 4 305 19.2 377.17 7.54 23.4
76 75 0.07896 0 12.83 0 0.437 6.273 6 4.2515 5 398 18.7 394.92 6.78 24.1
77 76 0.09512 0 12.83 0 0.437 6.286 45 4.5026 5 398 18.7 383.23 8.94 21.4
78 77 0.10153 0 12.83 0 0.437 6.279 74.5 4.0522 5 398 18.7 373.66 11.97 20
79 78 0.08707 0 12.83 0 0.437 6.14 45.8 4.0905 5 398 18.7 386.96 10.27 20.8
80 79 0.05646 0 12.83 0 0.437 6.232 53.7 5.0141 5 398 18.7 386.4 12.34 21.2
81 80 0.08387 0 12.83 0 0.437 5.874 36.6 4.5026 5 398 18.7 396.06 9.1 20.3
82 81 0.04113 25 4.86 0 0.426 6.727 33.5 5.4007 4 281 19 396.9 5.29 28
83 82 0.04462 25 4.86 0 0.426 6.619 70.4 5.4007 4 281 19 395.63 7.22 23.9
84 83 0.03659 25 4.86 0 0.426 6.302 32.2 5.4007 4 281 19 396.9 6.72 24.8
85 84 0.03551 25 4.86 0 0.426 6.167 46.7 5.4007 4 281 19 390.64 7.51 22.9
86 85 0.05059 0 4.49 0 0.449 6.389 48 4.7794 3 247 18.5 396.9 9.62 23.9
87 86 0.05735 0 4.49 0 0.449 6.63 56.1 4.4377 3 247 18.5 392.3 6.53 26.6
88 87 0.05188 0 4.49 0 0.449 6.015 45.1 4.4272 3 247 18.5 395.99 12.86 22.5
89 88 0.07151 0 4.49 0 0.449 6.121 56.8 3.7476 3 247 18.5 395.15 8.44 22.2
90 89 0.0566 0 3.41 0 0.489 7.007 86.3 3.4217 2 270 17.8 396.9 5.5 23.6
91 90 0.05302 0 3.41 0 0.489 7.079 63.1 3.4145 2 270 17.8 396.06 5.7 28.7
92 91 0.04684 0 3.41 0 0.489 6.417 66.1 3.0923 2 270 17.8 392.18 8.81 22.6
93 92 0.03932 0 3.41 0 0.489 6.405 73.9 3.0921 2 270 17.8 393.55 8.2 22
94 93 0.04203 28 15.04 0 0.464 6.442 53.6 3.6659 4 270 18.2 395.01 8.16 22.9
95 94 0.02875 28 15.04 0 0.464 6.211 28.9 3.6659 4 270 18.2 396.33 6.21 25
96 95 0.04294 28 15.04 0 0.464 6.249 77.3 3.615 4 270 18.2 396.9 10.59 20.6
97 96 0.12204 0 2.89 0 0.445 6.625 57.8 3.4952 2 276 18 357.98 6.65 28.4
98 97 0.11504 0 2.89 0 0.445 6.163 69.6 3.4952 2 276 18 391.83 11.34 21.4
99 98 0.12083 0 2.89 0 0.445 8.069 76 3.4952 2 276 18 396.9 4.21 38.7
100 99 0.08187 0 2.89 0 0.445 7.82 36.9 3.4952 2 276 18 393.53 3.57 43.8
101 100 0.0686 0 2.89 0 0.445 7.416 62.5 3.4952 2 276 18 396.9 6.19 33.2
102 101 0.14866 0 8.56 0 0.52 6.727 79.9 2.7778 5 384 20.9 394.76 9.42 27.5
103 102 0.11432 0 8.56 0 0.52 6.781 71.3 2.8561 5 384 20.9 395.58 7.67 26.5
104 103 0.22876 0 8.56 0 0.52 6.405 85.4 2.7147 5 384 20.9 70.8 10.63 18.6
105 104 0.21161 0 8.56 0 0.52 6.137 87.4 2.7147 5 384 20.9 394.47 13.44 19.3
106 105 0.1396 0 8.56 0 0.52 6.167 90 2.421 5 384 20.9 392.69 12.33 20.1
107 106 0.13262 0 8.56 0 0.52 5.851 96.7 2.1069 5 384 20.9 394.05 16.47 19.5
108 107 0.1712 0 8.56 0 0.52 5.836 91.9 2.211 5 384 20.9 395.67 18.66 19.5
109 108 0.13117 0 8.56 0 0.52 6.127 85.2 2.1224 5 384 20.9 387.69 14.09 20.4
110 109 0.12802 0 8.56 0 0.52 6.474 97.1 2.4329 5 384 20.9 395.24 12.27 19.8
111 110 0.26363 0 8.56 0 0.52 6.229 91.2 2.5451 5 384 20.9 391.23 15.55 19.4
112 111 0.10793 0 8.56 0 0.52 6.195 54.4 2.7778 5 384 20.9 393.49 13 21.7
113 112 0.10084 0 10.01 0 0.547 6.715 81.6 2.6775 6 432 17.8 395.59 10.16 22.8
114 113 0.12329 0 10.01 0 0.547 5.913 92.9 2.3534 6 432 17.8 394.95 16.21 18.8
115 114 0.22212 0 10.01 0 0.547 6.092 95.4 2.548 6 432 17.8 396.9 17.09 18.7
116 115 0.14231 0 10.01 0 0.547 6.254 84.2 2.2565 6 432 17.8 388.74 10.45 18.5
117 116 0.17134 0 10.01 0 0.547 5.928 88.2 2.4631 6 432 17.8 344.91 15.76 18.3
118 117 0.13158 0 10.01 0 0.547 6.176 72.5 2.7301 6 432 17.8 393.3 12.04 21.2
119 118 0.15098 0 10.01 0 0.547 6.021 82.6 2.7474 6 432 17.8 394.51 10.3 19.2
120 119 0.13058 0 10.01 0 0.547 5.872 73.1 2.4775 6 432 17.8 338.63 15.37 20.4
121 120 0.14476 0 10.01 0 0.547 5.731 65.2 2.7592 6 432 17.8 391.5 13.61 19.3
122 121 0.06899 0 25.65 0 0.581 5.87 69.7 2.2577 2 188 19.1 389.15 14.37 22
123 122 0.07165 0 25.65 0 0.581 6.004 84.1 2.1974 2 188 19.1 377.67 14.27 20.3
124 123 0.09299 0 25.65 0 0.581 5.961 92.9 2.0869 2 188 19.1 378.09 17.93 20.5
125 124 0.15038 0 25.65 0 0.581 5.856 97 1.9444 2 188 19.1 370.31 25.41 17.3
126 125 0.09849 0 25.65 0 0.581 5.879 95.8 2.0063 2 188 19.1 379.38 17.58 18.8
127 126 0.16902 0 25.65 0 0.581 5.986 88.4 1.9929 2 188 19.1 385.02 14.81 21.4
128 127 0.38735 0 25.65 0 0.581 5.613 95.6 1.7572 2 188 19.1 359.29 27.26 15.7
129 128 0.25915 0 21.89 0 0.624 5.693 96 1.7883 4 437 21.2 392.11 17.19 16.2
130 129 0.32543 0 21.89 0 0.624 6.431 98.8 1.8125 4 437 21.2 396.9 15.39 18
131 130 0.88125 0 21.89 0 0.624 5.637 94.7 1.9799 4 437 21.2 396.9 18.34 14.3
132 131 0.34006 0 21.89 0 0.624 6.458 98.9 2.1185 4 437 21.2 395.04 12.6 19.2
133 132 1.19294 0 21.89 0 0.624 6.326 97.7 2.271 4 437 21.2 396.9 12.26 19.6
134 133 0.59005 0 21.89 0 0.624 6.372 97.9 2.3274 4 437 21.2 385.76 11.12 23
135 134 0.32982 0 21.89 0 0.624 5.822 95.4 2.4699 4 437 21.2 388.69 15.03 18.4
136 135 0.97617 0 21.89 0 0.624 5.757 98.4 2.346 4 437 21.2 262.76 17.31 15.6
137 136 0.55778 0 21.89 0 0.624 6.335 98.2 2.1107 4 437 21.2 394.67 16.96 18.1
138 137 0.32264 0 21.89 0 0.624 5.942 93.5 1.9669 4 437 21.2 378.25 16.9 17.4
139 138 0.35233 0 21.89 0 0.624 6.454 98.4 1.8498 4 437 21.2 394.08 14.59 17.1
140 139 0.2498 0 21.89 0 0.624 5.857 98.2 1.6686 4 437 21.2 392.04 21.32 13.3
141 140 0.54452 0 21.89 0 0.624 6.151 97.9 1.6687 4 437 21.2 396.9 18.46 17.8
142 141 0.2909 0 21.89 0 0.624 6.174 93.6 1.6119 4 437 21.2 388.08 24.16 14
143 142 1.62864 0 21.89 0 0.624 5.019 100 1.4394 4 437 21.2 396.9 34.41 14.4
144 143 3.32105 0 19.58 1 0.871 5.403 100 1.3216 5 403 14.7 396.9 26.82 13.4
145 144 4.0974 0 19.58 0 0.871 5.468 100 1.4118 5 403 14.7 396.9 26.42 15.6
146 145 2.77974 0 19.58 0 0.871 4.903 97.8 1.3459 5 403 14.7 396.9 29.29 11.8
147 146 2.37934 0 19.58 0 0.871 6.13 100 1.4191 5 403 14.7 172.91 27.8 13.8
148 147 2.15505 0 19.58 0 0.871 5.628 100 1.5166 5 403 14.7 169.27 16.65 15.6
149 148 2.36862 0 19.58 0 0.871 4.926 95.7 1.4608 5 403 14.7 391.71 29.53 14.6
150 149 2.33099 0 19.58 0 0.871 5.186 93.8 1.5296 5 403 14.7 356.99 28.32 17.8
151 150 2.73397 0 19.58 0 0.871 5.597 94.9 1.5257 5 403 14.7 351.85 21.45 15.4
152 151 1.6566 0 19.58 0 0.871 6.122 97.3 1.618 5 403 14.7 372.8 14.1 21.5
153 152 1.49632 0 19.58 0 0.871 5.404 100 1.5916 5 403 14.7 341.6 13.28 19.6
154 153 1.12658 0 19.58 1 0.871 5.012 88 1.6102 5 403 14.7 343.28 12.12 15.3
155 154 2.14918 0 19.58 0 0.871 5.709 98.5 1.6232 5 403 14.7 261.95 15.79 19.4
156 155 1.41385 0 19.58 1 0.871 6.129 96 1.7494 5 403 14.7 321.02 15.12 17
157 156 3.53501 0 19.58 1 0.871 6.152 82.6 1.7455 5 403 14.7 88.01 15.02 15.6
158 157 2.44668 0 19.58 0 0.871 5.272 94 1.7364 5 403 14.7 88.63 16.14 13.1
159 158 1.22358 0 19.58 0 0.605 6.943 97.4 1.8773 5 403 14.7 363.43 4.59 41.3
160 159 1.34284 0 19.58 0 0.605 6.066 100 1.7573 5 403 14.7 353.89 6.43 24.3
161 160 1.42502 0 19.58 0 0.871 6.51 100 1.7659 5 403 14.7 364.31 7.39 23.3
162 161 1.27346 0 19.58 1 0.605 6.25 92.6 1.7984 5 403 14.7 338.92 5.5 27
163 162 1.46336 0 19.58 0 0.605 7.489 90.8 1.9709 5 403 14.7 374.43 1.73 50
164 163 1.83377 0 19.58 1 0.605 7.802 98.2 2.0407 5 403 14.7 389.61 1.92 50
165 164 1.51902 0 19.58 1 0.605 8.375 93.9 2.162 5 403 14.7 388.45 3.32 50
166 165 2.24236 0 19.58 0 0.605 5.854 91.8 2.422 5 403 14.7 395.11 11.64 22.7
167 166 2.924 0 19.58 0 0.605 6.101 93 2.2834 5 403 14.7 240.16 9.81 25
168 167 2.01019 0 19.58 0 0.605 7.929 96.2 2.0459 5 403 14.7 369.3 3.7 50
169 168 1.80028 0 19.58 0 0.605 5.877 79.2 2.4259 5 403 14.7 227.61 12.14 23.8
170 169 2.3004 0 19.58 0 0.605 6.319 96.1 2.1 5 403 14.7 297.09 11.1 23.8
171 170 2.44953 0 19.58 0 0.605 6.402 95.2 2.2625 5 403 14.7 330.04 11.32 22.3
172 171 1.20742 0 19.58 0 0.605 5.875 94.6 2.4259 5 403 14.7 292.29 14.43 17.4
173 172 2.3139 0 19.58 0 0.605 5.88 97.3 2.3887 5 403 14.7 348.13 12.03 19.1
174 173 0.13914 0 4.05 0 0.51 5.572 88.5 2.5961 5 296 16.6 396.9 14.69 23.1
175 174 0.09178 0 4.05 0 0.51 6.416 84.1 2.6463 5 296 16.6 395.5 9.04 23.6
176 175 0.08447 0 4.05 0 0.51 5.859 68.7 2.7019 5 296 16.6 393.23 9.64 22.6
177 176 0.06664 0 4.05 0 0.51 6.546 33.1 3.1323 5 296 16.6 390.96 5.33 29.4
178 177 0.07022 0 4.05 0 0.51 6.02 47.2 3.5549 5 296 16.6 393.23 10.11 23.2
179 178 0.05425 0 4.05 0 0.51 6.315 73.4 3.3175 5 296 16.6 395.6 6.29 24.6
180 179 0.06642 0 4.05 0 0.51 6.86 74.4 2.9153 5 296 16.6 391.27 6.92 29.9
181 180 0.0578 0 2.46 0 0.488 6.98 58.4 2.829 3 193 17.8 396.9 5.04 37.2
182 181 0.06588 0 2.46 0 0.488 7.765 83.3 2.741 3 193 17.8 395.56 7.56 39.8
183 182 0.06888 0 2.46 0 0.488 6.144 62.2 2.5979 3 193 17.8 396.9 9.45 36.2
184 183 0.09103 0 2.46 0 0.488 7.155 92.2 2.7006 3 193 17.8 394.12 4.82 37.9
185 184 0.10008 0 2.46 0 0.488 6.563 95.6 2.847 3 193 17.8 396.9 5.68 32.5
186 185 0.08308 0 2.46 0 0.488 5.604 89.8 2.9879 3 193 17.8 391 13.98 26.4
187 186 0.06047 0 2.46 0 0.488 6.153 68.8 3.2797 3 193 17.8 387.11 13.15 29.6
188 187 0.05602 0 2.46 0 0.488 7.831 53.6 3.1992 3 193 17.8 392.63 4.45 50
189 188 0.07875 45 3.44 0 0.437 6.782 41.1 3.7886 5 398 15.2 393.87 6.68 32
190 189 0.12579 45 3.44 0 0.437 6.556 29.1 4.5667 5 398 15.2 382.84 4.56 29.8
191 190 0.0837 45 3.44 0 0.437 7.185 38.9 4.5667 5 398 15.2 396.9 5.39 34.9
192 191 0.09068 45 3.44 0 0.437 6.951 21.5 6.4798 5 398 15.2 377.68 5.1 37
193 192 0.06911 45 3.44 0 0.437 6.739 30.8 6.4798 5 398 15.2 389.71 4.69 30.5
194 193 0.08664 45 3.44 0 0.437 7.178 26.3 6.4798 5 398 15.2 390.49 2.87 36.4
195 194 0.02187 60 2.93 0 0.401 6.8 9.9 6.2196 1 265 15.6 393.37 5.03 31.1
196 195 0.01439 60 2.93 0 0.401 6.604 18.8 6.2196 1 265 15.6 376.7 4.38 29.1
197 196 0.01381 80 0.46 0 0.422 7.875 32 5.6484 4 255 14.4 394.23 2.97 50
198 197 0.04011 80 1.52 0 0.404 7.287 34.1 7.309 2 329 12.6 396.9 4.08 33.3
199 198 0.04666 80 1.52 0 0.404 7.107 36.6 7.309 2 329 12.6 354.31 8.61 30.3
200 199 0.03768 80 1.52 0 0.404 7.274 38.3 7.309 2 329 12.6 392.2 6.62 34.6
201 200 0.0315 95 1.47 0 0.403 6.975 15.3 7.6534 3 402 17 396.9 4.56 34.9
202 201 0.01778 95 1.47 0 0.403 7.135 13.9 7.6534 3 402 17 384.3 4.45 32.9
203 202 0.03445 82.5 2.03 0 0.415 6.162 38.4 6.27 2 348 14.7 393.77 7.43 24.1
204 203 0.02177 82.5 2.03 0 0.415 7.61 15.7 6.27 2 348 14.7 395.38 3.11 42.3
205 204 0.0351 95 2.68 0 0.4161 7.853 33.2 5.118 4 224 14.7 392.78 3.81 48.5
206 205 0.02009 95 2.68 0 0.4161 8.034 31.9 5.118 4 224 14.7 390.55 2.88 50
207 206 0.13642 0 10.59 0 0.489 5.891 22.3 3.9454 4 277 18.6 396.9 10.87 22.6
208 207 0.22969 0 10.59 0 0.489 6.326 52.5 4.3549 4 277 18.6 394.87 10.97 24.4
209 208 0.25199 0 10.59 0 0.489 5.783 72.7 4.3549 4 277 18.6 389.43 18.06 22.5
210 209 0.13587 0 10.59 1 0.489 6.064 59.1 4.2392 4 277 18.6 381.32 14.66 24.4
211 210 0.43571 0 10.59 1 0.489 5.344 100 3.875 4 277 18.6 396.9 23.09 20
212 211 0.17446 0 10.59 1 0.489 5.96 92.1 3.8771 4 277 18.6 393.25 17.27 21.7
213 212 0.37578 0 10.59 1 0.489 5.404 88.6 3.665 4 277 18.6 395.24 23.98 19.3
214 213 0.21719 0 10.59 1 0.489 5.807 53.8 3.6526 4 277 18.6 390.94 16.03 22.4
215 214 0.14052 0 10.59 0 0.489 6.375 32.3 3.9454 4 277 18.6 385.81 9.38 28.1
216 215 0.28955 0 10.59 0 0.489 5.412 9.8 3.5875 4 277 18.6 348.93 29.55 23.7
217 216 0.19802 0 10.59 0 0.489 6.182 42.4 3.9454 4 277 18.6 393.63 9.47 25
218 217 0.0456 0 13.89 1 0.55 5.888 56 3.1121 5 276 16.4 392.8 13.51 23.3
219 218 0.07013 0 13.89 0 0.55 6.642 85.1 3.4211 5 276 16.4 392.78 9.69 28.7
220 219 0.11069 0 13.89 1 0.55 5.951 93.8 2.8893 5 276 16.4 396.9 17.92 21.5
221 220 0.11425 0 13.89 1 0.55 6.373 92.4 3.3633 5 276 16.4 393.74 10.5 23
222 221 0.35809 0 6.2 1 0.507 6.951 88.5 2.8617 8 307 17.4 391.7 9.71 26.7
223 222 0.40771 0 6.2 1 0.507 6.164 91.3 3.048 8 307 17.4 395.24 21.46 21.7
224 223 0.62356 0 6.2 1 0.507 6.879 77.7 3.2721 8 307 17.4 390.39 9.93 27.5
225 224 0.6147 0 6.2 0 0.507 6.618 80.8 3.2721 8 307 17.4 396.9 7.6 30.1
226 225 0.31533 0 6.2 0 0.504 8.266 78.3 2.8944 8 307 17.4 385.05 4.14 44.8
227 226 0.52693 0 6.2 0 0.504 8.725 83 2.8944 8 307 17.4 382 4.63 50
228 227 0.38214 0 6.2 0 0.504 8.04 86.5 3.2157 8 307 17.4 387.38 3.13 37.6
229 228 0.41238 0 6.2 0 0.504 7.163 79.9 3.2157 8 307 17.4 372.08 6.36 31.6
230 229 0.29819 0 6.2 0 0.504 7.686 17 3.3751 8 307 17.4 377.51 3.92 46.7
231 230 0.44178 0 6.2 0 0.504 6.552 21.4 3.3751 8 307 17.4 380.34 3.76 31.5
232 231 0.537 0 6.2 0 0.504 5.981 68.1 3.6715 8 307 17.4 378.35 11.65 24.3
233 232 0.46296 0 6.2 0 0.504 7.412 76.9 3.6715 8 307 17.4 376.14 5.25 31.7
234 233 0.57529 0 6.2 0 0.507 8.337 73.3 3.8384 8 307 17.4 385.91 2.47 41.7
235 234 0.33147 0 6.2 0 0.507 8.247 70.4 3.6519 8 307 17.4 378.95 3.95 48.3
236 235 0.44791 0 6.2 1 0.507 6.726 66.5 3.6519 8 307 17.4 360.2 8.05 29
237 236 0.33045 0 6.2 0 0.507 6.086 61.5 3.6519 8 307 17.4 376.75 10.88 24
238 237 0.52058 0 6.2 1 0.507 6.631 76.5 4.148 8 307 17.4 388.45 9.54 25.1
239 238 0.51183 0 6.2 0 0.507 7.358 71.6 4.148 8 307 17.4 390.07 4.73 31.5
240 239 0.08244 30 4.93 0 0.428 6.481 18.5 6.1899 6 300 16.6 379.41 6.36 23.7
241 240 0.09252 30 4.93 0 0.428 6.606 42.2 6.1899 6 300 16.6 383.78 7.37 23.3
242 241 0.11329 30 4.93 0 0.428 6.897 54.3 6.3361 6 300 16.6 391.25 11.38 22
243 242 0.10612 30 4.93 0 0.428 6.095 65.1 6.3361 6 300 16.6 394.62 12.4 20.1
244 243 0.1029 30 4.93 0 0.428 6.358 52.9 7.0355 6 300 16.6 372.75 11.22 22.2
245 244 0.12757 30 4.93 0 0.428 6.393 7.8 7.0355 6 300 16.6 374.71 5.19 23.7
246 245 0.20608 22 5.86 0 0.431 5.593 76.5 7.9549 7 330 19.1 372.49 12.5 17.6
247 246 0.19133 22 5.86 0 0.431 5.605 70.2 7.9549 7 330 19.1 389.13 18.46 18.5
248 247 0.33983 22 5.86 0 0.431 6.108 34.9 8.0555 7 330 19.1 390.18 9.16 24.3
249 248 0.19657 22 5.86 0 0.431 6.226 79.2 8.0555 7 330 19.1 376.14 10.15 20.5
250 249 0.16439 22 5.86 0 0.431 6.433 49.1 7.8265 7 330 19.1 374.71 9.52 24.5
251 250 0.19073 22 5.86 0 0.431 6.718 17.5 7.8265 7 330 19.1 393.74 6.56 26.2
252 251 0.1403 22 5.86 0 0.431 6.487 13 7.3967 7 330 19.1 396.28 5.9 24.4
253 252 0.21409 22 5.86 0 0.431 6.438 8.9 7.3967 7 330 19.1 377.07 3.59 24.8
254 253 0.08221 22 5.86 0 0.431 6.957 6.8 8.9067 7 330 19.1 386.09 3.53 29.6
255 254 0.36894 22 5.86 0 0.431 8.259 8.4 8.9067 7 330 19.1 396.9 3.54 42.8
256 255 0.04819 80 3.64 0 0.392 6.108 32 9.2203 1 315 16.4 392.89 6.57 21.9
257 256 0.03548 80 3.64 0 0.392 5.876 19.1 9.2203 1 315 16.4 395.18 9.25 20.9
258 257 0.01538 90 3.75 0 0.394 7.454 34.2 6.3361 3 244 15.9 386.34 3.11 44
259 258 0.61154 20 3.97 0 0.647 8.704 86.9 1.801 5 264 13 389.7 5.12 50
260 259 0.66351 20 3.97 0 0.647 7.333 100 1.8946 5 264 13 383.29 7.79 36
261 260 0.65665 20 3.97 0 0.647 6.842 100 2.0107 5 264 13 391.93 6.9 30.1
262 261 0.54011 20 3.97 0 0.647 7.203 81.8 2.1121 5 264 13 392.8 9.59 33.8
263 262 0.53412 20 3.97 0 0.647 7.52 89.4 2.1398 5 264 13 388.37 7.26 43.1
264 263 0.52014 20 3.97 0 0.647 8.398 91.5 2.2885 5 264 13 386.86 5.91 48.8
265 264 0.82526 20 3.97 0 0.647 7.327 94.5 2.0788 5 264 13 393.42 11.25 31
266 265 0.55007 20 3.97 0 0.647 7.206 91.6 1.9301 5 264 13 387.89 8.1 36.5
267 266 0.76162 20 3.97 0 0.647 5.56 62.8 1.9865 5 264 13 392.4 10.45 22.8
268 267 0.7857 20 3.97 0 0.647 7.014 84.6 2.1329 5 264 13 384.07 14.79 30.7
269 268 0.57834 20 3.97 0 0.575 8.297 67 2.4216 5 264 13 384.54 7.44 50
270 269 0.5405 20 3.97 0 0.575 7.47 52.6 2.872 5 264 13 390.3 3.16 43.5
271 270 0.09065 20 6.96 1 0.464 5.92 61.5 3.9175 3 223 18.6 391.34 13.65 20.7
272 271 0.29916 20 6.96 0 0.464 5.856 42.1 4.429 3 223 18.6 388.65 13 21.1
273 272 0.16211 20 6.96 0 0.464 6.24 16.3 4.429 3 223 18.6 396.9 6.59 25.2
274 273 0.1146 20 6.96 0 0.464 6.538 58.7 3.9175 3 223 18.6 394.96 7.73 24.4
275 274 0.22188 20 6.96 1 0.464 7.691 51.8 4.3665 3 223 18.6 390.77 6.58 35.2
276 275 0.05644 40 6.41 1 0.447 6.758 32.9 4.0776 4 254 17.6 396.9 3.53 32.4
277 276 0.09604 40 6.41 0 0.447 6.854 42.8 4.2673 4 254 17.6 396.9 2.98 32
278 277 0.10469 40 6.41 1 0.447 7.267 49 4.7872 4 254 17.6 389.25 6.05 33.2
279 278 0.06127 40 6.41 1 0.447 6.826 27.6 4.8628 4 254 17.6 393.45 4.16 33.1
280 279 0.07978 40 6.41 0 0.447 6.482 32.1 4.1403 4 254 17.6 396.9 7.19 29.1
281 280 0.21038 20 3.33 0 0.4429 6.812 32.2 4.1007 5 216 14.9 396.9 4.85 35.1
282 281 0.03578 20 3.33 0 0.4429 7.82 64.5 4.6947 5 216 14.9 387.31 3.76 45.4
283 282 0.03705 20 3.33 0 0.4429 6.968 37.2 5.2447 5 216 14.9 392.23 4.59 35.4
284 283 0.06129 20 3.33 1 0.4429 7.645 49.7 5.2119 5 216 14.9 377.07 3.01 46
285 284 0.01501 90 1.21 1 0.401 7.923 24.8 5.885 1 198 13.6 395.52 3.16 50
286 285 0.00906 90 2.97 0 0.4 7.088 20.8 7.3073 1 285 15.3 394.72 7.85 32.2
287 286 0.01096 55 2.25 0 0.389 6.453 31.9 7.3073 1 300 15.3 394.72 8.23 22
288 287 0.01965 80 1.76 0 0.385 6.23 31.5 9.0892 1 241 18.2 341.6 12.93 20.1
289 288 0.03871 52.5 5.32 0 0.405 6.209 31.3 7.3172 6 293 16.6 396.9 7.14 23.2
290 289 0.0459 52.5 5.32 0 0.405 6.315 45.6 7.3172 6 293 16.6 396.9 7.6 22.3
291 290 0.04297 52.5 5.32 0 0.405 6.565 22.9 7.3172 6 293 16.6 371.72 9.51 24.8
292 291 0.03502 80 4.95 0 0.411 6.861 27.9 5.1167 4 245 19.2 396.9 3.33 28.5
293 292 0.07886 80 4.95 0 0.411 7.148 27.7 5.1167 4 245 19.2 396.9 3.56 37.3
294 293 0.03615 80 4.95 0 0.411 6.63 23.4 5.1167 4 245 19.2 396.9 4.7 27.9
295 294 0.08265 0 13.92 0 0.437 6.127 18.4 5.5027 4 289 16 396.9 8.58 23.9
296 295 0.08199 0 13.92 0 0.437 6.009 42.3 5.5027 4 289 16 396.9 10.4 21.7
297 296 0.12932 0 13.92 0 0.437 6.678 31.1 5.9604 4 289 16 396.9 6.27 28.6
298 297 0.05372 0 13.92 0 0.437 6.549 51 5.9604 4 289 16 392.85 7.39 27.1
299 298 0.14103 0 13.92 0 0.437 5.79 58 6.32 4 289 16 396.9 15.84 20.3
300 299 0.06466 70 2.24 0 0.4 6.345 20.1 7.8278 5 358 14.8 368.24 4.97 22.5
301 300 0.05561 70 2.24 0 0.4 7.041 10 7.8278 5 358 14.8 371.58 4.74 29
302 301 0.04417 70 2.24 0 0.4 6.871 47.4 7.8278 5 358 14.8 390.86 6.07 24.8
303 302 0.03537 34 6.09 0 0.433 6.59 40.4 5.4917 7 329 16.1 395.75 9.5 22
304 303 0.09266 34 6.09 0 0.433 6.495 18.4 5.4917 7 329 16.1 383.61 8.67 26.4
305 304 0.1 34 6.09 0 0.433 6.982 17.7 5.4917 7 329 16.1 390.43 4.86 33.1
306 305 0.05515 33 2.18 0 0.472 7.236 41.1 4.022 7 222 18.4 393.68 6.93 36.1
307 306 0.05479 33 2.18 0 0.472 6.616 58.1 3.37 7 222 18.4 393.36 8.93 28.4
308 307 0.07503 33 2.18 0 0.472 7.42 71.9 3.0992 7 222 18.4 396.9 6.47 33.4
309 308 0.04932 33 2.18 0 0.472 6.849 70.3 3.1827 7 222 18.4 396.9 7.53 28.2
310 309 0.49298 0 9.9 0 0.544 6.635 82.5 3.3175 4 304 18.4 396.9 4.54 22.8
311 310 0.3494 0 9.9 0 0.544 5.972 76.7 3.1025 4 304 18.4 396.24 9.97 20.3
312 311 2.63548 0 9.9 0 0.544 4.973 37.8 2.5194 4 304 18.4 350.45 12.64 16.1
313 312 0.79041 0 9.9 0 0.544 6.122 52.8 2.6403 4 304 18.4 396.9 5.98 22.1
314 313 0.26169 0 9.9 0 0.544 6.023 90.4 2.834 4 304 18.4 396.3 11.72 19.4
315 314 0.26938 0 9.9 0 0.544 6.266 82.8 3.2628 4 304 18.4 393.39 7.9 21.6
316 315 0.3692 0 9.9 0 0.544 6.567 87.3 3.6023 4 304 18.4 395.69 9.28 23.8
317 316 0.25356 0 9.9 0 0.544 5.705 77.7 3.945 4 304 18.4 396.42 11.5 16.2
318 317 0.31827 0 9.9 0 0.544 5.914 83.2 3.9986 4 304 18.4 390.7 18.33 17.8
319 318 0.24522 0 9.9 0 0.544 5.782 71.7 4.0317 4 304 18.4 396.9 15.94 19.8
320 319 0.40202 0 9.9 0 0.544 6.382 67.2 3.5325 4 304 18.4 395.21 10.36 23.1
321 320 0.47547 0 9.9 0 0.544 6.113 58.8 4.0019 4 304 18.4 396.23 12.73 21
322 321 0.1676 0 7.38 0 0.493 6.426 52.3 4.5404 5 287 19.6 396.9 7.2 23.8
323 322 0.18159 0 7.38 0 0.493 6.376 54.3 4.5404 5 287 19.6 396.9 6.87 23.1
324 323 0.35114 0 7.38 0 0.493 6.041 49.9 4.7211 5 287 19.6 396.9 7.7 20.4
325 324 0.28392 0 7.38 0 0.493 5.708 74.3 4.7211 5 287 19.6 391.13 11.74 18.5
326 325 0.34109 0 7.38 0 0.493 6.415 40.1 4.7211 5 287 19.6 396.9 6.12 25
327 326 0.19186 0 7.38 0 0.493 6.431 14.7 5.4159 5 287 19.6 393.68 5.08 24.6
328 327 0.30347 0 7.38 0 0.493 6.312 28.9 5.4159 5 287 19.6 396.9 6.15 23
329 328 0.24103 0 7.38 0 0.493 6.083 43.7 5.4159 5 287 19.6 396.9 12.79 22.2
330 329 0.06617 0 3.24 0 0.46 5.868 25.8 5.2146 4 430 16.9 382.44 9.97 19.3
331 330 0.06724 0 3.24 0 0.46 6.333 17.2 5.2146 4 430 16.9 375.21 7.34 22.6
332 331 0.04544 0 3.24 0 0.46 6.144 32.2 5.8736 4 430 16.9 368.57 9.09 19.8
333 332 0.05023 35 6.06 0 0.4379 5.706 28.4 6.6407 1 304 16.9 394.02 12.43 17.1
334 333 0.03466 35 6.06 0 0.4379 6.031 23.3 6.6407 1 304 16.9 362.25 7.83 19.4
335 334 0.05083 0 5.19 0 0.515 6.316 38.1 6.4584 5 224 20.2 389.71 5.68 22.2
336 335 0.03738 0 5.19 0 0.515 6.31 38.5 6.4584 5 224 20.2 389.4 6.75 20.7
337 336 0.03961 0 5.19 0 0.515 6.037 34.5 5.9853 5 224 20.2 396.9 8.01 21.1
338 337 0.03427 0 5.19 0 0.515 5.869 46.3 5.2311 5 224 20.2 396.9 9.8 19.5
339 338 0.03041 0 5.19 0 0.515 5.895 59.6 5.615 5 224 20.2 394.81 10.56 18.5
340 339 0.03306 0 5.19 0 0.515 6.059 37.3 4.8122 5 224 20.2 396.14 8.51 20.6
341 340 0.05497 0 5.19 0 0.515 5.985 45.4 4.8122 5 224 20.2 396.9 9.74 19
342 341 0.06151 0 5.19 0 0.515 5.968 58.5 4.8122 5 224 20.2 396.9 9.29 18.7
343 342 0.01301 35 1.52 0 0.442 7.241 49.3 7.0379 1 284 15.5 394.74 5.49 32.7
344 343 0.02498 0 1.89 0 0.518 6.54 59.7 6.2669 1 422 15.9 389.96 8.65 16.5
345 344 0.02543 55 3.78 0 0.484 6.696 56.4 5.7321 5 370 17.6 396.9 7.18 23.9
346 345 0.03049 55 3.78 0 0.484 6.874 28.1 6.4654 5 370 17.6 387.97 4.61 31.2
347 346 0.03113 0 4.39 0 0.442 6.014 48.5 8.0136 3 352 18.8 385.64 10.53 17.5
348 347 0.06162 0 4.39 0 0.442 5.898 52.3 8.0136 3 352 18.8 364.61 12.67 17.2
349 348 0.0187 85 4.15 0 0.429 6.516 27.7 8.5353 4 351 17.9 392.43 6.36 23.1
350 349 0.01501 80 2.01 0 0.435 6.635 29.7 8.344 4 280 17 390.94 5.99 24.5
351 350 0.02899 40 1.25 0 0.429 6.939 34.5 8.7921 1 335 19.7 389.85 5.89 26.6
352 351 0.06211 40 1.25 0 0.429 6.49 44.4 8.7921 1 335 19.7 396.9 5.98 22.9
353 352 0.0795 60 1.69 0 0.411 6.579 35.9 10.7103 4 411 18.3 370.78 5.49 24.1
354 353 0.07244 60 1.69 0 0.411 5.884 18.5 10.7103 4 411 18.3 392.33 7.79 18.6
355 354 0.01709 90 2.02 0 0.41 6.728 36.1 12.1265 5 187 17 384.46 4.5 30.1
356 355 0.04301 80 1.91 0 0.413 5.663 21.9 10.5857 4 334 22 382.8 8.05 18.2
357 356 0.10659 80 1.91 0 0.413 5.936 19.5 10.5857 4 334 22 376.04 5.57 20.6
358 357 8.98296 0 18.1 1 0.77 6.212 97.4 2.1222 24 666 20.2 377.73 17.6 17.8
359 358 3.8497 0 18.1 1 0.77 6.395 91 2.5052 24 666 20.2 391.34 13.27 21.7
360 359 5.20177 0 18.1 1 0.77 6.127 83.4 2.7227 24 666 20.2 395.43 11.48 22.7
361 360 4.26131 0 18.1 0 0.77 6.112 81.3 2.5091 24 666 20.2 390.74 12.67 22.6
362 361 4.54192 0 18.1 0 0.77 6.398 88 2.5182 24 666 20.2 374.56 7.79 25
363 362 3.83684 0 18.1 0 0.77 6.251 91.1 2.2955 24 666 20.2 350.65 14.19 19.9
364 363 3.67822 0 18.1 0 0.77 5.362 96.2 2.1036 24 666 20.2 380.79 10.19 20.8
365 364 4.22239 0 18.1 1 0.77 5.803 89 1.9047 24 666 20.2 353.04 14.64 16.8
366 365 3.47428 0 18.1 1 0.718 8.78 82.9 1.9047 24 666 20.2 354.55 5.29 21.9
367 366 4.55587 0 18.1 0 0.718 3.561 87.9 1.6132 24 666 20.2 354.7 7.12 27.5
368 367 3.69695 0 18.1 0 0.718 4.963 91.4 1.7523 24 666 20.2 316.03 14 21.9
369 368 13.5222 0 18.1 0 0.631 3.863 100 1.5106 24 666 20.2 131.42 13.33 23.1
370 369 4.89822 0 18.1 0 0.631 4.97 100 1.3325 24 666 20.2 375.52 3.26 50
371 370 5.66998 0 18.1 1 0.631 6.683 96.8 1.3567 24 666 20.2 375.33 3.73 50
372 371 6.53876 0 18.1 1 0.631 7.016 97.5 1.2024 24 666 20.2 392.05 2.96 50
373 372 9.2323 0 18.1 0 0.631 6.216 100 1.1691 24 666 20.2 366.15 9.53 50
374 373 8.26725 0 18.1 1 0.668 5.875 89.6 1.1296 24 666 20.2 347.88 8.88 50
375 374 11.1081 0 18.1 0 0.668 4.906 100 1.1742 24 666 20.2 396.9 34.77 13.8
376 375 18.4982 0 18.1 0 0.668 4.138 100 1.137 24 666 20.2 396.9 37.97 13.8
377 376 19.6091 0 18.1 0 0.671 7.313 97.9 1.3163 24 666 20.2 396.9 13.44 15
378 377 15.288 0 18.1 0 0.671 6.649 93.3 1.3449 24 666 20.2 363.02 23.24 13.9
379 378 9.82349 0 18.1 0 0.671 6.794 98.8 1.358 24 666 20.2 396.9 21.24 13.3
380 379 23.6482 0 18.1 0 0.671 6.38 96.2 1.3861 24 666 20.2 396.9 23.69 13.1
381 380 17.8667 0 18.1 0 0.671 6.223 100 1.3861 24 666 20.2 393.74 21.78 10.2
382 381 88.9762 0 18.1 0 0.671 6.968 91.9 1.4165 24 666 20.2 396.9 17.21 10.4
383 382 15.8744 0 18.1 0 0.671 6.545 99.1 1.5192 24 666 20.2 396.9 21.08 10.9
384 383 9.18702 0 18.1 0 0.7 5.536 100 1.5804 24 666 20.2 396.9 23.6 11.3
385 384 7.99248 0 18.1 0 0.7 5.52 100 1.5331 24 666 20.2 396.9 24.56 12.3
386 385 20.0849 0 18.1 0 0.7 4.368 91.2 1.4395 24 666 20.2 285.83 30.63 8.8
387 386 16.8118 0 18.1 0 0.7 5.277 98.1 1.4261 24 666 20.2 396.9 30.81 7.2
388 387 24.3938 0 18.1 0 0.7 4.652 100 1.4672 24 666 20.2 396.9 28.28 10.5
389 388 22.5971 0 18.1 0 0.7 5 89.5 1.5184 24 666 20.2 396.9 31.99 7.4
390 389 14.3337 0 18.1 0 0.7 4.88 100 1.5895 24 666 20.2 372.92 30.62 10.2
391 390 8.15174 0 18.1 0 0.7 5.39 98.9 1.7281 24 666 20.2 396.9 20.85 11.5
392 391 6.96215 0 18.1 0 0.7 5.713 97 1.9265 24 666 20.2 394.43 17.11 15.1
393 392 5.29305 0 18.1 0 0.7 6.051 82.5 2.1678 24 666 20.2 378.38 18.76 23.2
394 393 11.5779 0 18.1 0 0.7 5.036 97 1.77 24 666 20.2 396.9 25.68 9.7
395 394 8.64476 0 18.1 0 0.693 6.193 92.6 1.7912 24 666 20.2 396.9 15.17 13.8
396 395 13.3598 0 18.1 0 0.693 5.887 94.7 1.7821 24 666 20.2 396.9 16.35 12.7
397 396 8.71675 0 18.1 0 0.693 6.471 98.8 1.7257 24 666 20.2 391.98 17.12 13.1
398 397 5.87205 0 18.1 0 0.693 6.405 96 1.6768 24 666 20.2 396.9 19.37 12.5
399 398 7.67202 0 18.1 0 0.693 5.747 98.9 1.6334 24 666 20.2 393.1 19.92 8.5
400 399 38.3518 0 18.1 0 0.693 5.453 100 1.4896 24 666 20.2 396.9 30.59 5
401 400 9.91655 0 18.1 0 0.693 5.852 77.8 1.5004 24 666 20.2 338.16 29.97 6.3
402 401 25.0461 0 18.1 0 0.693 5.987 100 1.5888 24 666 20.2 396.9 26.77 5.6
403 402 14.2362 0 18.1 0 0.693 6.343 100 1.5741 24 666 20.2 396.9 20.32 7.2
404 403 9.59571 0 18.1 0 0.693 6.404 100 1.639 24 666 20.2 376.11 20.31 12.1
405 404 24.8017 0 18.1 0 0.693 5.349 96 1.7028 24 666 20.2 396.9 19.77 8.3
406 405 41.5292 0 18.1 0 0.693 5.531 85.4 1.6074 24 666 20.2 329.46 27.38 8.5
407 406 67.9208 0 18.1 0 0.693 5.683 100 1.4254 24 666 20.2 384.97 22.98 5
408 407 20.7162 0 18.1 0 0.659 4.138 100 1.1781 24 666 20.2 370.22 23.34 11.9
409 408 11.9511 0 18.1 0 0.659 5.608 100 1.2852 24 666 20.2 332.09 12.13 27.9
410 409 7.40389 0 18.1 0 0.597 5.617 97.9 1.4547 24 666 20.2 314.64 26.4 17.2
411 410 14.4383 0 18.1 0 0.597 6.852 100 1.4655 24 666 20.2 179.36 19.78 27.5
412 411 51.1358 0 18.1 0 0.597 5.757 100 1.413 24 666 20.2 2.6 10.11 15
413 412 14.0507 0 18.1 0 0.597 6.657 100 1.5275 24 666 20.2 35.05 21.22 17.2
414 413 18.811 0 18.1 0 0.597 4.628 100 1.5539 24 666 20.2 28.79 34.37 17.9
415 414 28.6558 0 18.1 0 0.597 5.155 100 1.5894 24 666 20.2 210.97 20.08 16.3
416 415 45.7461 0 18.1 0 0.693 4.519 100 1.6582 24 666 20.2 88.27 36.98 7
417 416 18.0846 0 18.1 0 0.679 6.434 100 1.8347 24 666 20.2 27.25 29.05 7.2
418 417 10.8342 0 18.1 0 0.679 6.782 90.8 1.8195 24 666 20.2 21.57 25.79 7.5
419 418 25.9406 0 18.1 0 0.679 5.304 89.1 1.6475 24 666 20.2 127.36 26.64 10.4
420 419 73.5341 0 18.1 0 0.679 5.957 100 1.8026 24 666 20.2 16.45 20.62 8.8
421 420 11.8123 0 18.1 0 0.718 6.824 76.5 1.794 24 666 20.2 48.45 22.74 8.4
422 421 11.0874 0 18.1 0 0.718 6.411 100 1.8589 24 666 20.2 318.75 15.02 16.7
423 422 7.02259 0 18.1 0 0.718 6.006 95.3 1.8746 24 666 20.2 319.98 15.7 14.2
424 423 12.0482 0 18.1 0 0.614 5.648 87.6 1.9512 24 666 20.2 291.55 14.1 20.8
425 424 7.05042 0 18.1 0 0.614 6.103 85.1 2.0218 24 666 20.2 2.52 23.29 13.4
426 425 8.79212 0 18.1 0 0.584 5.565 70.6 2.0635 24 666 20.2 3.65 17.16 11.7
427 426 15.8603 0 18.1 0 0.679 5.896 95.4 1.9096 24 666 20.2 7.68 24.39 8.3
428 427 12.2472 0 18.1 0 0.584 5.837 59.7 1.9976 24 666 20.2 24.65 15.69 10.2
429 428 37.6619 0 18.1 0 0.679 6.202 78.7 1.8629 24 666 20.2 18.82 14.52 10.9
430 429 7.36711 0 18.1 0 0.679 6.193 78.1 1.9356 24 666 20.2 96.73 21.52 11
431 430 9.33889 0 18.1 0 0.679 6.38 95.6 1.9682 24 666 20.2 60.72 24.08 9.5
432 431 8.49213 0 18.1 0 0.584 6.348 86.1 2.0527 24 666 20.2 83.45 17.64 14.5
433 432 10.0623 0 18.1 0 0.584 6.833 94.3 2.0882 24 666 20.2 81.33 19.69 14.1
434 433 6.44405 0 18.1 0 0.584 6.425 74.8 2.2004 24 666 20.2 97.95 12.03 16.1
435 434 5.58107 0 18.1 0 0.713 6.436 87.9 2.3158 24 666 20.2 100.19 16.22 14.3
436 435 13.9134 0 18.1 0 0.713 6.208 95 2.2222 24 666 20.2 100.63 15.17 11.7
437 436 11.1604 0 18.1 0 0.74 6.629 94.6 2.1247 24 666 20.2 109.85 23.27 13.4
438 437 14.4208 0 18.1 0 0.74 6.461 93.3 2.0026 24 666 20.2 27.49 18.05 9.6
439 438 15.1772 0 18.1 0 0.74 6.152 100 1.9142 24 666 20.2 9.32 26.45 8.7
440 439 13.6781 0 18.1 0 0.74 5.935 87.9 1.8206 24 666 20.2 68.95 34.02 8.4
441 440 9.39063 0 18.1 0 0.74 5.627 93.9 1.8172 24 666 20.2 396.9 22.88 12.8
442 441 22.0511 0 18.1 0 0.74 5.818 92.4 1.8662 24 666 20.2 391.45 22.11 10.5
443 442 9.72418 0 18.1 0 0.74 6.406 97.2 2.0651 24 666 20.2 385.96 19.52 17.1
444 443 5.66637 0 18.1 0 0.74 6.219 100 2.0048 24 666 20.2 395.69 16.59 18.4
445 444 9.96654 0 18.1 0 0.74 6.485 100 1.9784 24 666 20.2 386.73 18.85 15.4
446 445 12.8023 0 18.1 0 0.74 5.854 96.6 1.8956 24 666 20.2 240.52 23.79 10.8
447 446 10.6718 0 18.1 0 0.74 6.459 94.8 1.9879 24 666 20.2 43.06 23.98 11.8
448 447 6.28807 0 18.1 0 0.74 6.341 96.4 2.072 24 666 20.2 318.01 17.79 14.9
449 448 9.92485 0 18.1 0 0.74 6.251 96.6 2.198 24 666 20.2 388.52 16.44 12.6
450 449 9.32909 0 18.1 0 0.713 6.185 98.7 2.2616 24 666 20.2 396.9 18.13 14.1
451 450 7.52601 0 18.1 0 0.713 6.417 98.3 2.185 24 666 20.2 304.21 19.31 13
452 451 6.71772 0 18.1 0 0.713 6.749 92.6 2.3236 24 666 20.2 0.32 17.44 13.4
453 452 5.44114 0 18.1 0 0.713 6.655 98.2 2.3552 24 666 20.2 355.29 17.73 15.2
454 453 5.09017 0 18.1 0 0.713 6.297 91.8 2.3682 24 666 20.2 385.09 17.27 16.1
455 454 8.24809 0 18.1 0 0.713 7.393 99.3 2.4527 24 666 20.2 375.87 16.74 17.8
456 455 9.51363 0 18.1 0 0.713 6.728 94.1 2.4961 24 666 20.2 6.68 18.71 14.9
457 456 4.75237 0 18.1 0 0.713 6.525 86.5 2.4358 24 666 20.2 50.92 18.13 14.1
458 457 4.66883 0 18.1 0 0.713 5.976 87.9 2.5806 24 666 20.2 10.48 19.01 12.7
459 458 8.20058 0 18.1 0 0.713 5.936 80.3 2.7792 24 666 20.2 3.5 16.94 13.5
460 459 7.75223 0 18.1 0 0.713 6.301 83.7 2.7831 24 666 20.2 272.21 16.23 14.9
461 460 6.80117 0 18.1 0 0.713 6.081 84.4 2.7175 24 666 20.2 396.9 14.7 20
462 461 4.81213 0 18.1 0 0.713 6.701 90 2.5975 24 666 20.2 255.23 16.42 16.4
463 462 3.69311 0 18.1 0 0.713 6.376 88.4 2.5671 24 666 20.2 391.43 14.65 17.7
464 463 6.65492 0 18.1 0 0.713 6.317 83 2.7344 24 666 20.2 396.9 13.99 19.5
465 464 5.82115 0 18.1 0 0.713 6.513 89.9 2.8016 24 666 20.2 393.82 10.29 20.2
466 465 7.83932 0 18.1 0 0.655 6.209 65.4 2.9634 24 666 20.2 396.9 13.22 21.4
467 466 3.1636 0 18.1 0 0.655 5.759 48.2 3.0665 24 666 20.2 334.4 14.13 19.9
468 467 3.77498 0 18.1 0 0.655 5.952 84.7 2.8715 24 666 20.2 22.01 17.15 19
469 468 4.42228 0 18.1 0 0.584 6.003 94.5 2.5403 24 666 20.2 331.29 21.32 19.1
470 469 15.5757 0 18.1 0 0.58 5.926 71 2.9084 24 666 20.2 368.74 18.13 19.1
471 470 13.0751 0 18.1 0 0.58 5.713 56.7 2.8237 24 666 20.2 396.9 14.76 20.1
472 471 4.34879 0 18.1 0 0.58 6.167 84 3.0334 24 666 20.2 396.9 16.29 19.9
473 472 4.03841 0 18.1 0 0.532 6.229 90.7 3.0993 24 666 20.2 395.33 12.87 19.6
474 473 3.56868 0 18.1 0 0.58 6.437 75 2.8965 24 666 20.2 393.37 14.36 23.2
475 474 4.64689 0 18.1 0 0.614 6.98 67.6 2.5329 24 666 20.2 374.68 11.66 29.8
476 475 8.05579 0 18.1 0 0.584 5.427 95.4 2.4298 24 666 20.2 352.58 18.14 13.8
477 476 6.39312 0 18.1 0 0.584 6.162 97.4 2.206 24 666 20.2 302.76 24.1 13.3
478 477 4.87141 0 18.1 0 0.614 6.484 93.6 2.3053 24 666 20.2 396.21 18.68 16.7
479 478 15.0234 0 18.1 0 0.614 5.304 97.3 2.1007 24 666 20.2 349.48 24.91 12
480 479 10.233 0 18.1 0 0.614 6.185 96.7 2.1705 24 666 20.2 379.7 18.03 14.6
481 480 14.3337 0 18.1 0 0.614 6.229 88 1.9512 24 666 20.2 383.32 13.11 21.4
482 481 5.82401 0 18.1 0 0.532 6.242 64.7 3.4242 24 666 20.2 396.9 10.74 23
483 482 5.70818 0 18.1 0 0.532 6.75 74.9 3.3317 24 666 20.2 393.07 7.74 23.7
484 483 5.73116 0 18.1 0 0.532 7.061 77 3.4106 24 666 20.2 395.28 7.01 25
485 484 2.81838 0 18.1 0 0.532 5.762 40.3 4.0983 24 666 20.2 392.92 10.42 21.8
486 485 2.37857 0 18.1 0 0.583 5.871 41.9 3.724 24 666 20.2 370.73 13.34 20.6
487 486 3.67367 0 18.1 0 0.583 6.312 51.9 3.9917 24 666 20.2 388.62 10.58 21.2
488 487 5.69175 0 18.1 0 0.583 6.114 79.8 3.5459 24 666 20.2 392.68 14.98 19.1
489 488 4.83567 0 18.1 0 0.583 5.905 53.2 3.1523 24 666 20.2 388.22 11.45 20.6
490 489 0.15086 0 27.74 0 0.609 5.454 92.7 1.8209 4 711 20.1 395.09 18.06 15.2
491 490 0.18337 0 27.74 0 0.609 5.414 98.3 1.7554 4 711 20.1 344.05 23.97 7
492 491 0.20746 0 27.74 0 0.609 5.093 98 1.8226 4 711 20.1 318.43 29.68 8.1
493 492 0.10574 0 27.74 0 0.609 5.983 98.8 1.8681 4 711 20.1 390.11 18.07 13.6
494 493 0.11132 0 27.74 0 0.609 5.983 83.5 2.1099 4 711 20.1 396.9 13.35 20.1
495 494 0.17331 0 9.69 0 0.585 5.707 54 2.3817 6 391 19.2 396.9 12.01 21.8
496 495 0.27957 0 9.69 0 0.585 5.926 42.6 2.3817 6 391 19.2 396.9 13.59 24.5
497 496 0.17899 0 9.69 0 0.585 5.67 28.8 2.7986 6 391 19.2 393.29 17.6 23.1
498 497 0.2896 0 9.69 0 0.585 5.39 72.9 2.7986 6 391 19.2 396.9 21.14 19.7
499 498 0.26838 0 9.69 0 0.585 5.794 70.6 2.8927 6 391 19.2 396.9 14.1 18.3
500 499 0.23912 0 9.69 0 0.585 6.019 65.3 2.4091 6 391 19.2 396.9 12.92 21.2
501 500 0.17783 0 9.69 0 0.585 5.569 73.5 2.3999 6 391 19.2 395.77 15.1 17.5
502 501 0.22438 0 9.69 0 0.585 6.027 79.7 2.4982 6 391 19.2 396.9 14.33 16.8
503 502 0.06263 0 11.93 0 0.573 6.593 69.1 2.4786 1 273 21 391.99 9.67 22.4
504 503 0.04527 0 11.93 0 0.573 6.12 76.7 2.2875 1 273 21 396.9 9.08 20.6
505 504 0.06076 0 11.93 0 0.573 6.976 91 2.1675 1 273 21 396.9 5.64 23.9
506 505 0.10959 0 11.93 0 0.573 6.794 89.3 2.3889 1 273 21 393.45 6.48 22
507 506 0.04741 0 11.93 0 0.573 6.03 80.8 2.505 1 273 21 396.9 7.88 11.9

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@ -0,0 +1,507 @@
CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PIRATIO,B,LSTAT,MEDV
0.00632,18.0,2.31,0,0.538,6.575,65.2,4.09,1,296.0,15.3,396.9,4.98,24.0
0.02731,0.0,7.07,0,0.469,6.421,78.9,4.9671,2,242.0,17.8,396.9,9.14,21.6
0.02729,0.0,7.07,0,0.469,7.185,61.1,4.9671,2,242.0,17.8,392.83,4.03,34.7
0.032369999999999996,0.0,2.18,0,0.458,6.998,45.8,6.0622,3,222.0,18.7,394.63,2.94,33.4
0.06905,0.0,2.18,0,0.458,7.147,54.2,6.0622,3,222.0,18.7,396.9,5.33,36.2
0.02985,0.0,2.18,0,0.458,6.43,58.7,6.0622,3,222.0,18.7,394.12,5.21,28.7
0.08829,12.5,7.87,0,0.524,6.012,66.6,5.5605,5,311.0,15.2,395.6,12.43,22.9
0.14455,12.5,7.87,0,0.524,6.172,96.1,5.9505,5,311.0,15.2,396.9,19.15,27.1
0.21124,12.5,7.87,0,0.524,5.631,100.0,6.0821,5,311.0,15.2,386.63,29.93,16.5
0.17004,12.5,7.87,0,0.524,6.004,85.9,6.5921,5,311.0,15.2,386.71,17.1,18.9
0.22489,12.5,7.87,0,0.524,6.377,94.3,6.3467,5,311.0,15.2,392.52,20.45,15.0
0.11747,12.5,7.87,0,0.524,6.009,82.9,6.2267,5,311.0,15.2,396.9,13.27,18.9
0.09378,12.5,7.87,0,0.524,5.889,39.0,5.4509,5,311.0,15.2,390.5,15.71,21.7
0.62976,0.0,8.14,0,0.538,5.949,61.8,4.7075,4,307.0,21.0,396.9,8.26,20.4
0.6379600000000001,0.0,8.14,0,0.538,6.096,84.5,4.4619,4,307.0,21.0,380.02,10.26,18.2
0.62739,0.0,8.14,0,0.538,5.834,56.5,4.4986,4,307.0,21.0,395.62,8.47,19.9
1.05393,0.0,8.14,0,0.538,5.935,29.3,4.4986,4,307.0,21.0,386.85,6.58,23.1
0.7842,0.0,8.14,0,0.538,5.99,81.7,4.2579,4,307.0,21.0,386.75,14.67,17.5
0.80271,0.0,8.14,0,0.538,5.456,36.6,3.7965,4,307.0,21.0,288.99,11.69,20.2
0.7258,0.0,8.14,0,0.538,5.727,69.5,3.7965,4,307.0,21.0,390.95,11.28,18.2
1.25179,0.0,8.14,0,0.538,5.57,98.1,3.7979,4,307.0,21.0,376.57,21.02,13.6
0.8520399999999999,0.0,8.14,0,0.538,5.965,89.2,4.0123,4,307.0,21.0,392.53,13.83,19.6
1.2324700000000002,0.0,8.14,0,0.538,6.142,91.7,3.9769,4,307.0,21.0,396.9,18.72,15.2
0.9884299999999999,0.0,8.14,0,0.538,5.813,100.0,4.0952,4,307.0,21.0,394.54,19.88,14.5
0.75026,0.0,8.14,0,0.538,5.924,94.1,4.3996,4,307.0,21.0,394.33,16.3,15.6
0.84054,0.0,8.14,0,0.538,5.599,85.7,4.4546,4,307.0,21.0,303.42,16.51,13.9
0.67191,0.0,8.14,0,0.538,5.813,90.3,4.682,4,307.0,21.0,376.88,14.81,16.6
0.9557700000000001,0.0,8.14,0,0.538,6.047,88.8,4.4534,4,307.0,21.0,306.38,17.28,14.8
0.77299,0.0,8.14,0,0.538,6.495,94.4,4.4547,4,307.0,21.0,387.94,12.8,18.4
1.00245,0.0,8.14,0,0.538,6.674,87.3,4.239,4,307.0,21.0,380.23,11.98,21.0
1.13081,0.0,8.14,0,0.538,5.713,94.1,4.233,4,307.0,21.0,360.17,22.6,12.7
1.3547200000000001,0.0,8.14,0,0.538,6.072,100.0,4.175,4,307.0,21.0,376.73,13.04,14.5
1.38799,0.0,8.14,0,0.538,5.95,82.0,3.99,4,307.0,21.0,232.6,27.71,13.2
1.15172,0.0,8.14,0,0.538,5.701,95.0,3.7872,4,307.0,21.0,358.77,18.35,13.1
1.6128200000000001,0.0,8.14,0,0.538,6.096,96.9,3.7598,4,307.0,21.0,248.31,20.34,13.5
0.06417,0.0,5.96,0,0.499,5.933,68.2,3.3603,5,279.0,19.2,396.9,9.68,18.9
0.09744,0.0,5.96,0,0.499,5.841,61.4,3.3779,5,279.0,19.2,377.56,11.41,20.0
0.08014,0.0,5.96,0,0.499,5.85,41.5,3.9342,5,279.0,19.2,396.9,8.77,21.0
0.17505,0.0,5.96,0,0.499,5.966,30.2,3.8473,5,279.0,19.2,393.43,10.13,24.7
0.027630000000000002,75.0,2.95,0,0.428,6.595,21.8,5.4011,3,252.0,18.3,395.63,4.32,30.8
0.033589999999999995,75.0,2.95,0,0.428,7.024,15.8,5.4011,3,252.0,18.3,395.62,1.98,34.9
0.12744,0.0,6.91,0,0.448,6.77,2.9,5.7209,3,233.0,17.9,385.41,4.84,26.6
0.1415,0.0,6.91,0,0.448,6.169,6.6,5.7209,3,233.0,17.9,383.37,5.81,25.3
0.15936,0.0,6.91,0,0.448,6.211,6.5,5.7209,3,233.0,17.9,394.46,7.44,24.7
0.12269000000000001,0.0,6.91,0,0.448,6.069,40.0,5.7209,3,233.0,17.9,389.39,9.55,21.2
0.17142000000000002,0.0,6.91,0,0.448,5.682,33.8,5.1004,3,233.0,17.9,396.9,10.21,19.3
0.18836,0.0,6.91,0,0.448,5.786,33.3,5.1004,3,233.0,17.9,396.9,14.15,20.0
0.22926999999999997,0.0,6.91,0,0.448,6.03,85.5,5.6894,3,233.0,17.9,392.74,18.8,16.6
0.25387,0.0,6.91,0,0.448,5.399,95.3,5.87,3,233.0,17.9,396.9,30.81,14.4
0.21977,0.0,6.91,0,0.448,5.602,62.0,6.0877,3,233.0,17.9,396.9,16.2,19.4
0.08872999999999999,21.0,5.64,0,0.439,5.963,45.7,6.8147,4,243.0,16.8,395.56,13.45,19.7
0.04337,21.0,5.64,0,0.439,6.115,63.0,6.8147,4,243.0,16.8,393.97,9.43,20.5
0.0536,21.0,5.64,0,0.439,6.511,21.1,6.8147,4,243.0,16.8,396.9,5.28,25.0
0.04981,21.0,5.64,0,0.439,5.998,21.4,6.8147,4,243.0,16.8,396.9,8.43,23.4
0.0136,75.0,4.0,0,0.41,5.888,47.6,7.3197,3,469.0,21.1,396.9,14.8,18.9
0.01311,90.0,1.22,0,0.403,7.249,21.9,8.6966,5,226.0,17.9,395.93,4.81,35.4
0.02055,85.0,0.74,0,0.41,6.383,35.7,9.1876,2,313.0,17.3,396.9,5.77,24.7
0.01432,100.0,1.32,0,0.411,6.816,40.5,8.3248,5,256.0,15.1,392.9,3.95,31.6
0.15445,25.0,5.13,0,0.453,6.145,29.2,7.8148,8,284.0,19.7,390.68,6.86,23.3
0.10328,25.0,5.13,0,0.453,5.927,47.2,6.932,8,284.0,19.7,396.9,9.22,19.6
0.14932,25.0,5.13,0,0.453,5.741,66.2,7.2254,8,284.0,19.7,395.11,13.15,18.7
0.17171,25.0,5.13,0,0.453,5.966,93.4,6.8185,8,284.0,19.7,378.08,14.44,16.0
0.11027,25.0,5.13,0,0.453,6.456,67.8,7.2255,8,284.0,19.7,396.9,6.73,22.2
0.1265,25.0,5.13,0,0.453,6.762,43.4,7.9809,8,284.0,19.7,395.58,9.5,25.0
0.01951,17.5,1.38,0,0.4161,7.104,59.5,9.2229,3,216.0,18.6,393.24,8.05,33.0
0.03584,80.0,3.37,0,0.398,6.29,17.8,6.6115,4,337.0,16.1,396.9,4.67,23.5
0.043789999999999996,80.0,3.37,0,0.398,5.787,31.1,6.6115,4,337.0,16.1,396.9,10.24,19.4
0.05789,12.5,6.07,0,0.409,5.878,21.4,6.498,4,345.0,18.9,396.21,8.1,22.0
0.13554000000000002,12.5,6.07,0,0.409,5.594,36.8,6.498,4,345.0,18.9,396.9,13.09,17.4
0.12816,12.5,6.07,0,0.409,5.885,33.0,6.498,4,345.0,18.9,396.9,8.79,20.9
0.08826,0.0,10.81,0,0.413,6.417,6.6,5.2873,4,305.0,19.2,383.73,6.72,24.2
0.15875999999999998,0.0,10.81,0,0.413,5.961,17.5,5.2873,4,305.0,19.2,376.94,9.88,21.7
0.09164,0.0,10.81,0,0.413,6.065,7.8,5.2873,4,305.0,19.2,390.91,5.52,22.8
0.19539,0.0,10.81,0,0.413,6.245,6.2,5.2873,4,305.0,19.2,377.17,7.54,23.4
0.07896,0.0,12.83,0,0.437,6.273,6.0,4.2515,5,398.0,18.7,394.92,6.78,24.1
0.09512000000000001,0.0,12.83,0,0.437,6.286,45.0,4.5026,5,398.0,18.7,383.23,8.94,21.4
0.10153,0.0,12.83,0,0.437,6.279,74.5,4.0522,5,398.0,18.7,373.66,11.97,20.0
0.08707000000000001,0.0,12.83,0,0.437,6.14,45.8,4.0905,5,398.0,18.7,386.96,10.27,20.8
0.05646,0.0,12.83,0,0.437,6.232,53.7,5.0141,5,398.0,18.7,386.4,12.34,21.2
0.08387,0.0,12.83,0,0.437,5.874,36.6,4.5026,5,398.0,18.7,396.06,9.1,20.3
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0.14231,0.0,10.01,0,0.547,6.254,84.2,2.2565,6,432.0,17.8,388.74,10.45,18.5
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0.13158,0.0,10.01,0,0.547,6.176,72.5,2.7301,6,432.0,17.8,393.3,12.04,21.2
0.15098,0.0,10.01,0,0.547,6.021,82.6,2.7474,6,432.0,17.8,394.51,10.3,19.2
0.13058,0.0,10.01,0,0.547,5.872,73.1,2.4775,6,432.0,17.8,338.63,15.37,20.4
0.14476,0.0,10.01,0,0.547,5.731,65.2,2.7592,6,432.0,17.8,391.5,13.61,19.3
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0.09299,0.0,25.65,0,0.581,5.961,92.9,2.0869,2,188.0,19.1,378.09,17.93,20.5
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0.09849,0.0,25.65,0,0.581,5.879,95.8,2.0063,2,188.0,19.1,379.38,17.58,18.8
0.16902,0.0,25.65,0,0.581,5.986,88.4,1.9929,2,188.0,19.1,385.02,14.81,21.4
0.38735,0.0,25.65,0,0.581,5.613,95.6,1.7572,2,188.0,19.1,359.29,27.26,15.7
0.25915,0.0,21.89,0,0.624,5.693,96.0,1.7883,4,437.0,21.2,392.11,17.19,16.2
0.32543,0.0,21.89,0,0.624,6.431,98.8,1.8125,4,437.0,21.2,396.9,15.39,18.0
0.88125,0.0,21.89,0,0.624,5.637,94.7,1.9799,4,437.0,21.2,396.9,18.34,14.3
0.34006,0.0,21.89,0,0.624,6.458,98.9,2.1185,4,437.0,21.2,395.04,12.6,19.2
1.19294,0.0,21.89,0,0.624,6.326,97.7,2.271,4,437.0,21.2,396.9,12.26,19.6
0.59005,0.0,21.89,0,0.624,6.372,97.9,2.3274,4,437.0,21.2,385.76,11.12,23.0
0.32982,0.0,21.89,0,0.624,5.822,95.4,2.4699,4,437.0,21.2,388.69,15.03,18.4
0.9761700000000001,0.0,21.89,0,0.624,5.757,98.4,2.346,4,437.0,21.2,262.76,17.31,15.6
0.55778,0.0,21.89,0,0.624,6.335,98.2,2.1107,4,437.0,21.2,394.67,16.96,18.1
0.32264,0.0,21.89,0,0.624,5.942,93.5,1.9669,4,437.0,21.2,378.25,16.9,17.4
0.35233000000000003,0.0,21.89,0,0.624,6.454,98.4,1.8498,4,437.0,21.2,394.08,14.59,17.1
0.2498,0.0,21.89,0,0.624,5.857,98.2,1.6686,4,437.0,21.2,392.04,21.32,13.3
0.54452,0.0,21.89,0,0.624,6.151,97.9,1.6687,4,437.0,21.2,396.9,18.46,17.8
0.2909,0.0,21.89,0,0.624,6.174,93.6,1.6119,4,437.0,21.2,388.08,24.16,14.0
1.6286399999999999,0.0,21.89,0,0.624,5.019,100.0,1.4394,4,437.0,21.2,396.9,34.41,14.4
3.32105,0.0,19.58,1,0.871,5.403,100.0,1.3216,5,403.0,14.7,396.9,26.82,13.4
4.0974,0.0,19.58,0,0.871,5.468,100.0,1.4118,5,403.0,14.7,396.9,26.42,15.6
2.7797400000000003,0.0,19.58,0,0.871,4.903,97.8,1.3459,5,403.0,14.7,396.9,29.29,11.8
2.37934,0.0,19.58,0,0.871,6.13,100.0,1.4191,5,403.0,14.7,172.91,27.8,13.8
2.15505,0.0,19.58,0,0.871,5.628,100.0,1.5166,5,403.0,14.7,169.27,16.65,15.6
2.36862,0.0,19.58,0,0.871,4.926,95.7,1.4608,5,403.0,14.7,391.71,29.53,14.6
2.3309900000000003,0.0,19.58,0,0.871,5.186,93.8,1.5296,5,403.0,14.7,356.99,28.32,17.8
2.7339700000000002,0.0,19.58,0,0.871,5.597,94.9,1.5257,5,403.0,14.7,351.85,21.45,15.4
1.6566,0.0,19.58,0,0.871,6.122,97.3,1.618,5,403.0,14.7,372.8,14.1,21.5
1.49632,0.0,19.58,0,0.871,5.404,100.0,1.5916,5,403.0,14.7,341.6,13.28,19.6
1.12658,0.0,19.58,1,0.871,5.012,88.0,1.6102,5,403.0,14.7,343.28,12.12,15.3
2.14918,0.0,19.58,0,0.871,5.709,98.5,1.6232,5,403.0,14.7,261.95,15.79,19.4
1.41385,0.0,19.58,1,0.871,6.129,96.0,1.7494,5,403.0,14.7,321.02,15.12,17.0
3.5350099999999998,0.0,19.58,1,0.871,6.152,82.6,1.7455,5,403.0,14.7,88.01,15.02,15.6
2.4466799999999997,0.0,19.58,0,0.871,5.272,94.0,1.7364,5,403.0,14.7,88.63,16.14,13.1
1.22358,0.0,19.58,0,0.605,6.943,97.4,1.8773,5,403.0,14.7,363.43,4.59,41.3
1.34284,0.0,19.58,0,0.605,6.066,100.0,1.7573,5,403.0,14.7,353.89,6.43,24.3
1.4250200000000002,0.0,19.58,0,0.871,6.51,100.0,1.7659,5,403.0,14.7,364.31,7.39,23.3
1.27346,0.0,19.58,1,0.605,6.25,92.6,1.7984,5,403.0,14.7,338.92,5.5,27.0
1.46336,0.0,19.58,0,0.605,7.489,90.8,1.9709,5,403.0,14.7,374.43,1.73,50.0
1.8337700000000001,0.0,19.58,1,0.605,7.802,98.2,2.0407,5,403.0,14.7,389.61,1.92,50.0
1.51902,0.0,19.58,1,0.605,8.375,93.9,2.162,5,403.0,14.7,388.45,3.32,50.0
2.2423599999999997,0.0,19.58,0,0.605,5.854,91.8,2.422,5,403.0,14.7,395.11,11.64,22.7
2.924,0.0,19.58,0,0.605,6.101,93.0,2.2834,5,403.0,14.7,240.16,9.81,25.0
2.01019,0.0,19.58,0,0.605,7.929,96.2,2.0459,5,403.0,14.7,369.3,3.7,50.0
1.8002799999999999,0.0,19.58,0,0.605,5.877,79.2,2.4259,5,403.0,14.7,227.61,12.14,23.8
2.3004,0.0,19.58,0,0.605,6.319,96.1,2.1,5,403.0,14.7,297.09,11.1,23.8
2.4495299999999998,0.0,19.58,0,0.605,6.402,95.2,2.2625,5,403.0,14.7,330.04,11.32,22.3
1.2074200000000002,0.0,19.58,0,0.605,5.875,94.6,2.4259,5,403.0,14.7,292.29,14.43,17.4
2.3139,0.0,19.58,0,0.605,5.88,97.3,2.3887,5,403.0,14.7,348.13,12.03,19.1
0.13914,0.0,4.05,0,0.51,5.572,88.5,2.5961,5,296.0,16.6,396.9,14.69,23.1
0.09178,0.0,4.05,0,0.51,6.416,84.1,2.6463,5,296.0,16.6,395.5,9.04,23.6
0.08447,0.0,4.05,0,0.51,5.859,68.7,2.7019,5,296.0,16.6,393.23,9.64,22.6
0.06663999999999999,0.0,4.05,0,0.51,6.546,33.1,3.1323,5,296.0,16.6,390.96,5.33,29.4
0.07022,0.0,4.05,0,0.51,6.02,47.2,3.5549,5,296.0,16.6,393.23,10.11,23.2
0.05425,0.0,4.05,0,0.51,6.315,73.4,3.3175,5,296.0,16.6,395.6,6.29,24.6
0.06642,0.0,4.05,0,0.51,6.86,74.4,2.9153,5,296.0,16.6,391.27,6.92,29.9
0.0578,0.0,2.46,0,0.488,6.98,58.4,2.829,3,193.0,17.8,396.9,5.04,37.2
0.06588,0.0,2.46,0,0.488,7.765,83.3,2.741,3,193.0,17.8,395.56,7.56,39.8
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0.09103,0.0,2.46,0,0.488,7.155,92.2,2.7006,3,193.0,17.8,394.12,4.82,37.9
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0.06047,0.0,2.46,0,0.488,6.153,68.8,3.2797,3,193.0,17.8,387.11,13.15,29.6
0.05602000000000001,0.0,2.46,0,0.488,7.831,53.6,3.1992,3,193.0,17.8,392.63,4.45,50.0
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0.12579,45.0,3.44,0,0.437,6.556,29.1,4.5667,5,398.0,15.2,382.84,4.56,29.8
0.0837,45.0,3.44,0,0.437,7.185,38.9,4.5667,5,398.0,15.2,396.9,5.39,34.9
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0.06911,45.0,3.44,0,0.437,6.739,30.8,6.4798,5,398.0,15.2,389.71,4.69,30.5
0.08664,45.0,3.44,0,0.437,7.178,26.3,6.4798,5,398.0,15.2,390.49,2.87,36.4
0.02187,60.0,2.93,0,0.401,6.8,9.9,6.2196,1,265.0,15.6,393.37,5.03,31.1
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0.03445,82.5,2.03,0,0.415,6.162,38.4,6.27,2,348.0,14.7,393.77,7.43,24.1
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0.22969,0.0,10.59,0,0.489,6.326,52.5,4.3549,4,277.0,18.6,394.87,10.97,24.4
0.25199,0.0,10.59,0,0.489,5.783,72.7,4.3549,4,277.0,18.6,389.43,18.06,22.5
0.13587,0.0,10.59,1,0.489,6.064,59.1,4.2392,4,277.0,18.6,381.32,14.66,24.4
0.43571000000000004,0.0,10.59,1,0.489,5.344,100.0,3.875,4,277.0,18.6,396.9,23.09,20.0
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0.21719000000000002,0.0,10.59,1,0.489,5.807,53.8,3.6526,4,277.0,18.6,390.94,16.03,22.4
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13.5222,0.0,18.1,0,0.631,3.863,100.0,1.5106,24,666.0,20.2,131.42,13.33,23.1
4.898219999999999,0.0,18.1,0,0.631,4.97,100.0,1.3325,24,666.0,20.2,375.52,3.26,50.0
5.669980000000001,0.0,18.1,1,0.631,6.683,96.8,1.3567,24,666.0,20.2,375.33,3.73,50.0
6.53876,0.0,18.1,1,0.631,7.016,97.5,1.2024,24,666.0,20.2,392.05,2.96,50.0
9.2323,0.0,18.1,0,0.631,6.216,100.0,1.1691,24,666.0,20.2,366.15,9.53,50.0
8.26725,0.0,18.1,1,0.668,5.875,89.6,1.1296,24,666.0,20.2,347.88,8.88,50.0
11.1081,0.0,18.1,0,0.668,4.906,100.0,1.1742,24,666.0,20.2,396.9,34.77,13.8
18.4982,0.0,18.1,0,0.668,4.138,100.0,1.137,24,666.0,20.2,396.9,37.97,13.8
19.6091,0.0,18.1,0,0.671,7.313,97.9,1.3163,24,666.0,20.2,396.9,13.44,15.0
15.288,0.0,18.1,0,0.671,6.649,93.3,1.3449,24,666.0,20.2,363.02,23.24,13.9
9.82349,0.0,18.1,0,0.671,6.794,98.8,1.358,24,666.0,20.2,396.9,21.24,13.3
23.6482,0.0,18.1,0,0.671,6.38,96.2,1.3861,24,666.0,20.2,396.9,23.69,13.1
17.8667,0.0,18.1,0,0.671,6.223,100.0,1.3861,24,666.0,20.2,393.74,21.78,10.2
88.9762,0.0,18.1,0,0.671,6.968,91.9,1.4165,24,666.0,20.2,396.9,17.21,10.4
15.8744,0.0,18.1,0,0.671,6.545,99.1,1.5192,24,666.0,20.2,396.9,21.08,10.9
9.18702,0.0,18.1,0,0.7,5.536,100.0,1.5804,24,666.0,20.2,396.9,23.6,11.3
7.9924800000000005,0.0,18.1,0,0.7,5.52,100.0,1.5331,24,666.0,20.2,396.9,24.56,12.3
20.0849,0.0,18.1,0,0.7,4.368,91.2,1.4395,24,666.0,20.2,285.83,30.63,8.8
16.8118,0.0,18.1,0,0.7,5.277,98.1,1.4261,24,666.0,20.2,396.9,30.81,7.2
24.3938,0.0,18.1,0,0.7,4.652,100.0,1.4672,24,666.0,20.2,396.9,28.28,10.5
22.5971,0.0,18.1,0,0.7,5.0,89.5,1.5184,24,666.0,20.2,396.9,31.99,7.4
14.3337,0.0,18.1,0,0.7,4.88,100.0,1.5895,24,666.0,20.2,372.92,30.62,10.2
8.15174,0.0,18.1,0,0.7,5.39,98.9,1.7281,24,666.0,20.2,396.9,20.85,11.5
6.96215,0.0,18.1,0,0.7,5.713,97.0,1.9265,24,666.0,20.2,394.43,17.11,15.1
5.29305,0.0,18.1,0,0.7,6.051,82.5,2.1678,24,666.0,20.2,378.38,18.76,23.2
11.5779,0.0,18.1,0,0.7,5.036,97.0,1.77,24,666.0,20.2,396.9,25.68,9.7
8.64476,0.0,18.1,0,0.693,6.193,92.6,1.7912,24,666.0,20.2,396.9,15.17,13.8
13.3598,0.0,18.1,0,0.693,5.887,94.7,1.7821,24,666.0,20.2,396.9,16.35,12.7
8.71675,0.0,18.1,0,0.693,6.471,98.8,1.7257,24,666.0,20.2,391.98,17.12,13.1
5.87205,0.0,18.1,0,0.693,6.405,96.0,1.6768,24,666.0,20.2,396.9,19.37,12.5
7.67202,0.0,18.1,0,0.693,5.747,98.9,1.6334,24,666.0,20.2,393.1,19.92,8.5
38.3518,0.0,18.1,0,0.693,5.453,100.0,1.4896,24,666.0,20.2,396.9,30.59,5.0
9.91655,0.0,18.1,0,0.693,5.852,77.8,1.5004,24,666.0,20.2,338.16,29.97,6.3
25.0461,0.0,18.1,0,0.693,5.987,100.0,1.5888,24,666.0,20.2,396.9,26.77,5.6
14.2362,0.0,18.1,0,0.693,6.343,100.0,1.5741,24,666.0,20.2,396.9,20.32,7.2
9.59571,0.0,18.1,0,0.693,6.404,100.0,1.639,24,666.0,20.2,376.11,20.31,12.1
24.8017,0.0,18.1,0,0.693,5.349,96.0,1.7028,24,666.0,20.2,396.9,19.77,8.3
41.5292,0.0,18.1,0,0.693,5.531,85.4,1.6074,24,666.0,20.2,329.46,27.38,8.5
67.9208,0.0,18.1,0,0.693,5.683,100.0,1.4254,24,666.0,20.2,384.97,22.98,5.0
20.7162,0.0,18.1,0,0.659,4.138,100.0,1.1781,24,666.0,20.2,370.22,23.34,11.9
11.9511,0.0,18.1,0,0.659,5.608,100.0,1.2852,24,666.0,20.2,332.09,12.13,27.9
7.40389,0.0,18.1,0,0.597,5.617,97.9,1.4547,24,666.0,20.2,314.64,26.4,17.2
14.4383,0.0,18.1,0,0.597,6.852,100.0,1.4655,24,666.0,20.2,179.36,19.78,27.5
51.1358,0.0,18.1,0,0.597,5.757,100.0,1.413,24,666.0,20.2,2.6,10.11,15.0
14.0507,0.0,18.1,0,0.597,6.657,100.0,1.5275,24,666.0,20.2,35.05,21.22,17.2
18.811,0.0,18.1,0,0.597,4.628,100.0,1.5539,24,666.0,20.2,28.79,34.37,17.9
28.6558,0.0,18.1,0,0.597,5.155,100.0,1.5894,24,666.0,20.2,210.97,20.08,16.3
45.7461,0.0,18.1,0,0.693,4.519,100.0,1.6582,24,666.0,20.2,88.27,36.98,7.0
18.0846,0.0,18.1,0,0.679,6.434,100.0,1.8347,24,666.0,20.2,27.25,29.05,7.2
10.8342,0.0,18.1,0,0.679,6.782,90.8,1.8195,24,666.0,20.2,21.57,25.79,7.5
25.9406,0.0,18.1,0,0.679,5.304,89.1,1.6475,24,666.0,20.2,127.36,26.64,10.4
73.5341,0.0,18.1,0,0.679,5.957,100.0,1.8026,24,666.0,20.2,16.45,20.62,8.8
11.8123,0.0,18.1,0,0.718,6.824,76.5,1.794,24,666.0,20.2,48.45,22.74,8.4
11.0874,0.0,18.1,0,0.718,6.411,100.0,1.8589,24,666.0,20.2,318.75,15.02,16.7
7.022589999999999,0.0,18.1,0,0.718,6.006,95.3,1.8746,24,666.0,20.2,319.98,15.7,14.2
12.0482,0.0,18.1,0,0.614,5.648,87.6,1.9512,24,666.0,20.2,291.55,14.1,20.8
7.05042,0.0,18.1,0,0.614,6.103,85.1,2.0218,24,666.0,20.2,2.52,23.29,13.4
8.792119999999999,0.0,18.1,0,0.584,5.565,70.6,2.0635,24,666.0,20.2,3.65,17.16,11.7
15.8603,0.0,18.1,0,0.679,5.896,95.4,1.9096,24,666.0,20.2,7.68,24.39,8.3
12.2472,0.0,18.1,0,0.584,5.837,59.7,1.9976,24,666.0,20.2,24.65,15.69,10.2
37.6619,0.0,18.1,0,0.679,6.202,78.7,1.8629,24,666.0,20.2,18.82,14.52,10.9
7.36711,0.0,18.1,0,0.679,6.193,78.1,1.9356,24,666.0,20.2,96.73,21.52,11.0
9.33889,0.0,18.1,0,0.679,6.38,95.6,1.9682,24,666.0,20.2,60.72,24.08,9.5
8.49213,0.0,18.1,0,0.584,6.348,86.1,2.0527,24,666.0,20.2,83.45,17.64,14.5
10.0623,0.0,18.1,0,0.584,6.833,94.3,2.0882,24,666.0,20.2,81.33,19.69,14.1
6.44405,0.0,18.1,0,0.584,6.425,74.8,2.2004,24,666.0,20.2,97.95,12.03,16.1
5.5810699999999995,0.0,18.1,0,0.713,6.436,87.9,2.3158,24,666.0,20.2,100.19,16.22,14.3
13.9134,0.0,18.1,0,0.713,6.208,95.0,2.2222,24,666.0,20.2,100.63,15.17,11.7
11.1604,0.0,18.1,0,0.74,6.629,94.6,2.1247,24,666.0,20.2,109.85,23.27,13.4
14.4208,0.0,18.1,0,0.74,6.461,93.3,2.0026,24,666.0,20.2,27.49,18.05,9.6
15.1772,0.0,18.1,0,0.74,6.152,100.0,1.9142,24,666.0,20.2,9.32,26.45,8.7
13.6781,0.0,18.1,0,0.74,5.935,87.9,1.8206,24,666.0,20.2,68.95,34.02,8.4
9.39063,0.0,18.1,0,0.74,5.627,93.9,1.8172,24,666.0,20.2,396.9,22.88,12.8
22.0511,0.0,18.1,0,0.74,5.818,92.4,1.8662,24,666.0,20.2,391.45,22.11,10.5
9.72418,0.0,18.1,0,0.74,6.406,97.2,2.0651,24,666.0,20.2,385.96,19.52,17.1
5.66637,0.0,18.1,0,0.74,6.219,100.0,2.0048,24,666.0,20.2,395.69,16.59,18.4
9.96654,0.0,18.1,0,0.74,6.485,100.0,1.9784,24,666.0,20.2,386.73,18.85,15.4
12.8023,0.0,18.1,0,0.74,5.854,96.6,1.8956,24,666.0,20.2,240.52,23.79,10.8
10.6718,0.0,18.1,0,0.74,6.459,94.8,1.9879,24,666.0,20.2,43.06,23.98,11.8
6.288069999999999,0.0,18.1,0,0.74,6.341,96.4,2.072,24,666.0,20.2,318.01,17.79,14.9
9.92485,0.0,18.1,0,0.74,6.251,96.6,2.198,24,666.0,20.2,388.52,16.44,12.6
9.329089999999999,0.0,18.1,0,0.713,6.185,98.7,2.2616,24,666.0,20.2,396.9,18.13,14.1
7.52601,0.0,18.1,0,0.713,6.417,98.3,2.185,24,666.0,20.2,304.21,19.31,13.0
6.71772,0.0,18.1,0,0.713,6.749,92.6,2.3236,24,666.0,20.2,0.32,17.44,13.4
5.44114,0.0,18.1,0,0.713,6.655,98.2,2.3552,24,666.0,20.2,355.29,17.73,15.2
5.09017,0.0,18.1,0,0.713,6.297,91.8,2.3682,24,666.0,20.2,385.09,17.27,16.1
8.24809,0.0,18.1,0,0.713,7.393,99.3,2.4527,24,666.0,20.2,375.87,16.74,17.8
9.513630000000001,0.0,18.1,0,0.713,6.728,94.1,2.4961,24,666.0,20.2,6.68,18.71,14.9
4.75237,0.0,18.1,0,0.713,6.525,86.5,2.4358,24,666.0,20.2,50.92,18.13,14.1
4.668830000000001,0.0,18.1,0,0.713,5.976,87.9,2.5806,24,666.0,20.2,10.48,19.01,12.7
8.20058,0.0,18.1,0,0.713,5.936,80.3,2.7792,24,666.0,20.2,3.5,16.94,13.5
7.75223,0.0,18.1,0,0.713,6.301,83.7,2.7831,24,666.0,20.2,272.21,16.23,14.9
6.80117,0.0,18.1,0,0.713,6.081,84.4,2.7175,24,666.0,20.2,396.9,14.7,20.0
4.812130000000001,0.0,18.1,0,0.713,6.701,90.0,2.5975,24,666.0,20.2,255.23,16.42,16.4
3.69311,0.0,18.1,0,0.713,6.376,88.4,2.5671,24,666.0,20.2,391.43,14.65,17.7
6.65492,0.0,18.1,0,0.713,6.317,83.0,2.7344,24,666.0,20.2,396.9,13.99,19.5
5.82115,0.0,18.1,0,0.713,6.513,89.9,2.8016,24,666.0,20.2,393.82,10.29,20.2
7.83932,0.0,18.1,0,0.655,6.209,65.4,2.9634,24,666.0,20.2,396.9,13.22,21.4
3.1636,0.0,18.1,0,0.655,5.759,48.2,3.0665,24,666.0,20.2,334.4,14.13,19.9
3.7749800000000002,0.0,18.1,0,0.655,5.952,84.7,2.8715,24,666.0,20.2,22.01,17.15,19.0
4.422280000000001,0.0,18.1,0,0.584,6.003,94.5,2.5403,24,666.0,20.2,331.29,21.32,19.1
15.5757,0.0,18.1,0,0.58,5.926,71.0,2.9084,24,666.0,20.2,368.74,18.13,19.1
13.0751,0.0,18.1,0,0.58,5.713,56.7,2.8237,24,666.0,20.2,396.9,14.76,20.1
4.34879,0.0,18.1,0,0.58,6.167,84.0,3.0334,24,666.0,20.2,396.9,16.29,19.9
4.03841,0.0,18.1,0,0.532,6.229,90.7,3.0993,24,666.0,20.2,395.33,12.87,19.6
3.56868,0.0,18.1,0,0.58,6.437,75.0,2.8965,24,666.0,20.2,393.37,14.36,23.2
4.64689,0.0,18.1,0,0.614,6.98,67.6,2.5329,24,666.0,20.2,374.68,11.66,29.8
8.05579,0.0,18.1,0,0.584,5.427,95.4,2.4298,24,666.0,20.2,352.58,18.14,13.8
6.39312,0.0,18.1,0,0.584,6.162,97.4,2.206,24,666.0,20.2,302.76,24.1,13.3
4.87141,0.0,18.1,0,0.614,6.484,93.6,2.3053,24,666.0,20.2,396.21,18.68,16.7
15.0234,0.0,18.1,0,0.614,5.304,97.3,2.1007,24,666.0,20.2,349.48,24.91,12.0
10.233,0.0,18.1,0,0.614,6.185,96.7,2.1705,24,666.0,20.2,379.7,18.03,14.6
14.3337,0.0,18.1,0,0.614,6.229,88.0,1.9512,24,666.0,20.2,383.32,13.11,21.4
5.8240099999999995,0.0,18.1,0,0.532,6.242,64.7,3.4242,24,666.0,20.2,396.9,10.74,23.0
5.7081800000000005,0.0,18.1,0,0.532,6.75,74.9,3.3317,24,666.0,20.2,393.07,7.74,23.7
5.73116,0.0,18.1,0,0.532,7.061,77.0,3.4106,24,666.0,20.2,395.28,7.01,25.0
2.81838,0.0,18.1,0,0.532,5.762,40.3,4.0983,24,666.0,20.2,392.92,10.42,21.8
2.37857,0.0,18.1,0,0.583,5.871,41.9,3.724,24,666.0,20.2,370.73,13.34,20.6
3.6736699999999995,0.0,18.1,0,0.583,6.312,51.9,3.9917,24,666.0,20.2,388.62,10.58,21.2
5.69175,0.0,18.1,0,0.583,6.114,79.8,3.5459,24,666.0,20.2,392.68,14.98,19.1
4.8356699999999995,0.0,18.1,0,0.583,5.905,53.2,3.1523,24,666.0,20.2,388.22,11.45,20.6
0.15086,0.0,27.74,0,0.609,5.454,92.7,1.8209,4,711.0,20.1,395.09,18.06,15.2
0.18337,0.0,27.74,0,0.609,5.414,98.3,1.7554,4,711.0,20.1,344.05,23.97,7.0
0.20745999999999998,0.0,27.74,0,0.609,5.093,98.0,1.8226,4,711.0,20.1,318.43,29.68,8.1
0.10574000000000001,0.0,27.74,0,0.609,5.983,98.8,1.8681,4,711.0,20.1,390.11,18.07,13.6
0.11132,0.0,27.74,0,0.609,5.983,83.5,2.1099,4,711.0,20.1,396.9,13.35,20.1
0.17331,0.0,9.69,0,0.585,5.707,54.0,2.3817,6,391.0,19.2,396.9,12.01,21.8
0.27957,0.0,9.69,0,0.585,5.926,42.6,2.3817,6,391.0,19.2,396.9,13.59,24.5
0.17899,0.0,9.69,0,0.585,5.67,28.8,2.7986,6,391.0,19.2,393.29,17.6,23.1
0.2896,0.0,9.69,0,0.585,5.39,72.9,2.7986,6,391.0,19.2,396.9,21.14,19.7
0.26838,0.0,9.69,0,0.585,5.794,70.6,2.8927,6,391.0,19.2,396.9,14.1,18.3
0.23911999999999997,0.0,9.69,0,0.585,6.019,65.3,2.4091,6,391.0,19.2,396.9,12.92,21.2
0.17783,0.0,9.69,0,0.585,5.569,73.5,2.3999,6,391.0,19.2,395.77,15.1,17.5
0.22438000000000002,0.0,9.69,0,0.585,6.027,79.7,2.4982,6,391.0,19.2,396.9,14.33,16.8
0.06262999999999999,0.0,11.93,0,0.573,6.593,69.1,2.4786,1,273.0,21.0,391.99,9.67,22.4
0.04527,0.0,11.93,0,0.573,6.12,76.7,2.2875,1,273.0,21.0,396.9,9.08,20.6
0.06076,0.0,11.93,0,0.573,6.976,91.0,2.1675,1,273.0,21.0,396.9,5.64,23.9
0.10959,0.0,11.93,0,0.573,6.794,89.3,2.3889,1,273.0,21.0,393.45,6.48,22.0
0.04741,0.0,11.93,0,0.573,6.03,80.8,2.505,1,273.0,21.0,396.9,7.88,11.9
1 CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PIRATIO B LSTAT MEDV
2 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.09 1 296.0 15.3 396.9 4.98 24.0
3 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242.0 17.8 396.9 9.14 21.6
4 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242.0 17.8 392.83 4.03 34.7
5 0.032369999999999996 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222.0 18.7 394.63 2.94 33.4
6 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222.0 18.7 396.9 5.33 36.2
7 0.02985 0.0 2.18 0 0.458 6.43 58.7 6.0622 3 222.0 18.7 394.12 5.21 28.7
8 0.08829 12.5 7.87 0 0.524 6.012 66.6 5.5605 5 311.0 15.2 395.6 12.43 22.9
9 0.14455 12.5 7.87 0 0.524 6.172 96.1 5.9505 5 311.0 15.2 396.9 19.15 27.1
10 0.21124 12.5 7.87 0 0.524 5.631 100.0 6.0821 5 311.0 15.2 386.63 29.93 16.5
11 0.17004 12.5 7.87 0 0.524 6.004 85.9 6.5921 5 311.0 15.2 386.71 17.1 18.9
12 0.22489 12.5 7.87 0 0.524 6.377 94.3 6.3467 5 311.0 15.2 392.52 20.45 15.0
13 0.11747 12.5 7.87 0 0.524 6.009 82.9 6.2267 5 311.0 15.2 396.9 13.27 18.9
14 0.09378 12.5 7.87 0 0.524 5.889 39.0 5.4509 5 311.0 15.2 390.5 15.71 21.7
15 0.62976 0.0 8.14 0 0.538 5.949 61.8 4.7075 4 307.0 21.0 396.9 8.26 20.4
16 0.6379600000000001 0.0 8.14 0 0.538 6.096 84.5 4.4619 4 307.0 21.0 380.02 10.26 18.2
17 0.62739 0.0 8.14 0 0.538 5.834 56.5 4.4986 4 307.0 21.0 395.62 8.47 19.9
18 1.05393 0.0 8.14 0 0.538 5.935 29.3 4.4986 4 307.0 21.0 386.85 6.58 23.1
19 0.7842 0.0 8.14 0 0.538 5.99 81.7 4.2579 4 307.0 21.0 386.75 14.67 17.5
20 0.80271 0.0 8.14 0 0.538 5.456 36.6 3.7965 4 307.0 21.0 288.99 11.69 20.2
21 0.7258 0.0 8.14 0 0.538 5.727 69.5 3.7965 4 307.0 21.0 390.95 11.28 18.2
22 1.25179 0.0 8.14 0 0.538 5.57 98.1 3.7979 4 307.0 21.0 376.57 21.02 13.6
23 0.8520399999999999 0.0 8.14 0 0.538 5.965 89.2 4.0123 4 307.0 21.0 392.53 13.83 19.6
24 1.2324700000000002 0.0 8.14 0 0.538 6.142 91.7 3.9769 4 307.0 21.0 396.9 18.72 15.2
25 0.9884299999999999 0.0 8.14 0 0.538 5.813 100.0 4.0952 4 307.0 21.0 394.54 19.88 14.5
26 0.75026 0.0 8.14 0 0.538 5.924 94.1 4.3996 4 307.0 21.0 394.33 16.3 15.6
27 0.84054 0.0 8.14 0 0.538 5.599 85.7 4.4546 4 307.0 21.0 303.42 16.51 13.9
28 0.67191 0.0 8.14 0 0.538 5.813 90.3 4.682 4 307.0 21.0 376.88 14.81 16.6
29 0.9557700000000001 0.0 8.14 0 0.538 6.047 88.8 4.4534 4 307.0 21.0 306.38 17.28 14.8
30 0.77299 0.0 8.14 0 0.538 6.495 94.4 4.4547 4 307.0 21.0 387.94 12.8 18.4
31 1.00245 0.0 8.14 0 0.538 6.674 87.3 4.239 4 307.0 21.0 380.23 11.98 21.0
32 1.13081 0.0 8.14 0 0.538 5.713 94.1 4.233 4 307.0 21.0 360.17 22.6 12.7
33 1.3547200000000001 0.0 8.14 0 0.538 6.072 100.0 4.175 4 307.0 21.0 376.73 13.04 14.5
34 1.38799 0.0 8.14 0 0.538 5.95 82.0 3.99 4 307.0 21.0 232.6 27.71 13.2
35 1.15172 0.0 8.14 0 0.538 5.701 95.0 3.7872 4 307.0 21.0 358.77 18.35 13.1
36 1.6128200000000001 0.0 8.14 0 0.538 6.096 96.9 3.7598 4 307.0 21.0 248.31 20.34 13.5
37 0.06417 0.0 5.96 0 0.499 5.933 68.2 3.3603 5 279.0 19.2 396.9 9.68 18.9
38 0.09744 0.0 5.96 0 0.499 5.841 61.4 3.3779 5 279.0 19.2 377.56 11.41 20.0
39 0.08014 0.0 5.96 0 0.499 5.85 41.5 3.9342 5 279.0 19.2 396.9 8.77 21.0
40 0.17505 0.0 5.96 0 0.499 5.966 30.2 3.8473 5 279.0 19.2 393.43 10.13 24.7
41 0.027630000000000002 75.0 2.95 0 0.428 6.595 21.8 5.4011 3 252.0 18.3 395.63 4.32 30.8
42 0.033589999999999995 75.0 2.95 0 0.428 7.024 15.8 5.4011 3 252.0 18.3 395.62 1.98 34.9
43 0.12744 0.0 6.91 0 0.448 6.77 2.9 5.7209 3 233.0 17.9 385.41 4.84 26.6
44 0.1415 0.0 6.91 0 0.448 6.169 6.6 5.7209 3 233.0 17.9 383.37 5.81 25.3
45 0.15936 0.0 6.91 0 0.448 6.211 6.5 5.7209 3 233.0 17.9 394.46 7.44 24.7
46 0.12269000000000001 0.0 6.91 0 0.448 6.069 40.0 5.7209 3 233.0 17.9 389.39 9.55 21.2
47 0.17142000000000002 0.0 6.91 0 0.448 5.682 33.8 5.1004 3 233.0 17.9 396.9 10.21 19.3
48 0.18836 0.0 6.91 0 0.448 5.786 33.3 5.1004 3 233.0 17.9 396.9 14.15 20.0
49 0.22926999999999997 0.0 6.91 0 0.448 6.03 85.5 5.6894 3 233.0 17.9 392.74 18.8 16.6
50 0.25387 0.0 6.91 0 0.448 5.399 95.3 5.87 3 233.0 17.9 396.9 30.81 14.4
51 0.21977 0.0 6.91 0 0.448 5.602 62.0 6.0877 3 233.0 17.9 396.9 16.2 19.4
52 0.08872999999999999 21.0 5.64 0 0.439 5.963 45.7 6.8147 4 243.0 16.8 395.56 13.45 19.7
53 0.04337 21.0 5.64 0 0.439 6.115 63.0 6.8147 4 243.0 16.8 393.97 9.43 20.5
54 0.0536 21.0 5.64 0 0.439 6.511 21.1 6.8147 4 243.0 16.8 396.9 5.28 25.0
55 0.04981 21.0 5.64 0 0.439 5.998 21.4 6.8147 4 243.0 16.8 396.9 8.43 23.4
56 0.0136 75.0 4.0 0 0.41 5.888 47.6 7.3197 3 469.0 21.1 396.9 14.8 18.9
57 0.01311 90.0 1.22 0 0.403 7.249 21.9 8.6966 5 226.0 17.9 395.93 4.81 35.4
58 0.02055 85.0 0.74 0 0.41 6.383 35.7 9.1876 2 313.0 17.3 396.9 5.77 24.7
59 0.01432 100.0 1.32 0 0.411 6.816 40.5 8.3248 5 256.0 15.1 392.9 3.95 31.6
60 0.15445 25.0 5.13 0 0.453 6.145 29.2 7.8148 8 284.0 19.7 390.68 6.86 23.3
61 0.10328 25.0 5.13 0 0.453 5.927 47.2 6.932 8 284.0 19.7 396.9 9.22 19.6
62 0.14932 25.0 5.13 0 0.453 5.741 66.2 7.2254 8 284.0 19.7 395.11 13.15 18.7
63 0.17171 25.0 5.13 0 0.453 5.966 93.4 6.8185 8 284.0 19.7 378.08 14.44 16.0
64 0.11027 25.0 5.13 0 0.453 6.456 67.8 7.2255 8 284.0 19.7 396.9 6.73 22.2
65 0.1265 25.0 5.13 0 0.453 6.762 43.4 7.9809 8 284.0 19.7 395.58 9.5 25.0
66 0.01951 17.5 1.38 0 0.4161 7.104 59.5 9.2229 3 216.0 18.6 393.24 8.05 33.0
67 0.03584 80.0 3.37 0 0.398 6.29 17.8 6.6115 4 337.0 16.1 396.9 4.67 23.5
68 0.043789999999999996 80.0 3.37 0 0.398 5.787 31.1 6.6115 4 337.0 16.1 396.9 10.24 19.4
69 0.05789 12.5 6.07 0 0.409 5.878 21.4 6.498 4 345.0 18.9 396.21 8.1 22.0
70 0.13554000000000002 12.5 6.07 0 0.409 5.594 36.8 6.498 4 345.0 18.9 396.9 13.09 17.4
71 0.12816 12.5 6.07 0 0.409 5.885 33.0 6.498 4 345.0 18.9 396.9 8.79 20.9
72 0.08826 0.0 10.81 0 0.413 6.417 6.6 5.2873 4 305.0 19.2 383.73 6.72 24.2
73 0.15875999999999998 0.0 10.81 0 0.413 5.961 17.5 5.2873 4 305.0 19.2 376.94 9.88 21.7
74 0.09164 0.0 10.81 0 0.413 6.065 7.8 5.2873 4 305.0 19.2 390.91 5.52 22.8
75 0.19539 0.0 10.81 0 0.413 6.245 6.2 5.2873 4 305.0 19.2 377.17 7.54 23.4
76 0.07896 0.0 12.83 0 0.437 6.273 6.0 4.2515 5 398.0 18.7 394.92 6.78 24.1
77 0.09512000000000001 0.0 12.83 0 0.437 6.286 45.0 4.5026 5 398.0 18.7 383.23 8.94 21.4
78 0.10153 0.0 12.83 0 0.437 6.279 74.5 4.0522 5 398.0 18.7 373.66 11.97 20.0
79 0.08707000000000001 0.0 12.83 0 0.437 6.14 45.8 4.0905 5 398.0 18.7 386.96 10.27 20.8
80 0.05646 0.0 12.83 0 0.437 6.232 53.7 5.0141 5 398.0 18.7 386.4 12.34 21.2
81 0.08387 0.0 12.83 0 0.437 5.874 36.6 4.5026 5 398.0 18.7 396.06 9.1 20.3
82 0.04113 25.0 4.86 0 0.426 6.727 33.5 5.4007 4 281.0 19.0 396.9 5.29 28.0
83 0.04462 25.0 4.86 0 0.426 6.619 70.4 5.4007 4 281.0 19.0 395.63 7.22 23.9
84 0.03659 25.0 4.86 0 0.426 6.302 32.2 5.4007 4 281.0 19.0 396.9 6.72 24.8
85 0.03551 25.0 4.86 0 0.426 6.167 46.7 5.4007 4 281.0 19.0 390.64 7.51 22.9
86 0.050589999999999996 0.0 4.49 0 0.449 6.389 48.0 4.7794 3 247.0 18.5 396.9 9.62 23.9
87 0.05735 0.0 4.49 0 0.449 6.63 56.1 4.4377 3 247.0 18.5 392.3 6.53 26.6
88 0.051879999999999996 0.0 4.49 0 0.449 6.015 45.1 4.4272 3 247.0 18.5 395.99 12.86 22.5
89 0.07151 0.0 4.49 0 0.449 6.121 56.8 3.7476 3 247.0 18.5 395.15 8.44 22.2
90 0.0566 0.0 3.41 0 0.489 7.007 86.3 3.4217 2 270.0 17.8 396.9 5.5 23.6
91 0.053020000000000005 0.0 3.41 0 0.489 7.079 63.1 3.4145 2 270.0 17.8 396.06 5.7 28.7
92 0.04684 0.0 3.41 0 0.489 6.417 66.1 3.0923 2 270.0 17.8 392.18 8.81 22.6
93 0.03932 0.0 3.41 0 0.489 6.405 73.9 3.0921 2 270.0 17.8 393.55 8.2 22.0
94 0.04203 28.0 15.04 0 0.464 6.442 53.6 3.6659 4 270.0 18.2 395.01 8.16 22.9
95 0.02875 28.0 15.04 0 0.464 6.211 28.9 3.6659 4 270.0 18.2 396.33 6.21 25.0
96 0.04294 28.0 15.04 0 0.464 6.249 77.3 3.615 4 270.0 18.2 396.9 10.59 20.6
97 0.12204000000000001 0.0 2.89 0 0.445 6.625 57.8 3.4952 2 276.0 18.0 357.98 6.65 28.4
98 0.11504 0.0 2.89 0 0.445 6.163 69.6 3.4952 2 276.0 18.0 391.83 11.34 21.4
99 0.12082999999999999 0.0 2.89 0 0.445 8.069 76.0 3.4952 2 276.0 18.0 396.9 4.21 38.7
100 0.08187 0.0 2.89 0 0.445 7.82 36.9 3.4952 2 276.0 18.0 393.53 3.57 43.8
101 0.0686 0.0 2.89 0 0.445 7.416 62.5 3.4952 2 276.0 18.0 396.9 6.19 33.2
102 0.14866 0.0 8.56 0 0.52 6.727 79.9 2.7778 5 384.0 20.9 394.76 9.42 27.5
103 0.11432 0.0 8.56 0 0.52 6.781 71.3 2.8561 5 384.0 20.9 395.58 7.67 26.5
104 0.22876 0.0 8.56 0 0.52 6.405 85.4 2.7147 5 384.0 20.9 70.8 10.63 18.6
105 0.21161 0.0 8.56 0 0.52 6.137 87.4 2.7147 5 384.0 20.9 394.47 13.44 19.3
106 0.1396 0.0 8.56 0 0.52 6.167 90.0 2.421 5 384.0 20.9 392.69 12.33 20.1
107 0.13262000000000002 0.0 8.56 0 0.52 5.851 96.7 2.1069 5 384.0 20.9 394.05 16.47 19.5
108 0.1712 0.0 8.56 0 0.52 5.836 91.9 2.211 5 384.0 20.9 395.67 18.66 19.5
109 0.13117 0.0 8.56 0 0.52 6.127 85.2 2.1224 5 384.0 20.9 387.69 14.09 20.4
110 0.12802 0.0 8.56 0 0.52 6.474 97.1 2.4329 5 384.0 20.9 395.24 12.27 19.8
111 0.26363000000000003 0.0 8.56 0 0.52 6.229 91.2 2.5451 5 384.0 20.9 391.23 15.55 19.4
112 0.10793 0.0 8.56 0 0.52 6.195 54.4 2.7778 5 384.0 20.9 393.49 13.0 21.7
113 0.10084 0.0 10.01 0 0.547 6.715 81.6 2.6775 6 432.0 17.8 395.59 10.16 22.8
114 0.12329000000000001 0.0 10.01 0 0.547 5.913 92.9 2.3534 6 432.0 17.8 394.95 16.21 18.8
115 0.22211999999999998 0.0 10.01 0 0.547 6.092 95.4 2.548 6 432.0 17.8 396.9 17.09 18.7
116 0.14231 0.0 10.01 0 0.547 6.254 84.2 2.2565 6 432.0 17.8 388.74 10.45 18.5
117 0.17134000000000002 0.0 10.01 0 0.547 5.928 88.2 2.4631 6 432.0 17.8 344.91 15.76 18.3
118 0.13158 0.0 10.01 0 0.547 6.176 72.5 2.7301 6 432.0 17.8 393.3 12.04 21.2
119 0.15098 0.0 10.01 0 0.547 6.021 82.6 2.7474 6 432.0 17.8 394.51 10.3 19.2
120 0.13058 0.0 10.01 0 0.547 5.872 73.1 2.4775 6 432.0 17.8 338.63 15.37 20.4
121 0.14476 0.0 10.01 0 0.547 5.731 65.2 2.7592 6 432.0 17.8 391.5 13.61 19.3
122 0.06899 0.0 25.65 0 0.581 5.87 69.7 2.2577 2 188.0 19.1 389.15 14.37 22.0
123 0.07165 0.0 25.65 0 0.581 6.004 84.1 2.1974 2 188.0 19.1 377.67 14.27 20.3
124 0.09299 0.0 25.65 0 0.581 5.961 92.9 2.0869 2 188.0 19.1 378.09 17.93 20.5
125 0.15037999999999999 0.0 25.65 0 0.581 5.856 97.0 1.9444 2 188.0 19.1 370.31 25.41 17.3
126 0.09849 0.0 25.65 0 0.581 5.879 95.8 2.0063 2 188.0 19.1 379.38 17.58 18.8
127 0.16902 0.0 25.65 0 0.581 5.986 88.4 1.9929 2 188.0 19.1 385.02 14.81 21.4
128 0.38735 0.0 25.65 0 0.581 5.613 95.6 1.7572 2 188.0 19.1 359.29 27.26 15.7
129 0.25915 0.0 21.89 0 0.624 5.693 96.0 1.7883 4 437.0 21.2 392.11 17.19 16.2
130 0.32543 0.0 21.89 0 0.624 6.431 98.8 1.8125 4 437.0 21.2 396.9 15.39 18.0
131 0.88125 0.0 21.89 0 0.624 5.637 94.7 1.9799 4 437.0 21.2 396.9 18.34 14.3
132 0.34006 0.0 21.89 0 0.624 6.458 98.9 2.1185 4 437.0 21.2 395.04 12.6 19.2
133 1.19294 0.0 21.89 0 0.624 6.326 97.7 2.271 4 437.0 21.2 396.9 12.26 19.6
134 0.59005 0.0 21.89 0 0.624 6.372 97.9 2.3274 4 437.0 21.2 385.76 11.12 23.0
135 0.32982 0.0 21.89 0 0.624 5.822 95.4 2.4699 4 437.0 21.2 388.69 15.03 18.4
136 0.9761700000000001 0.0 21.89 0 0.624 5.757 98.4 2.346 4 437.0 21.2 262.76 17.31 15.6
137 0.55778 0.0 21.89 0 0.624 6.335 98.2 2.1107 4 437.0 21.2 394.67 16.96 18.1
138 0.32264 0.0 21.89 0 0.624 5.942 93.5 1.9669 4 437.0 21.2 378.25 16.9 17.4
139 0.35233000000000003 0.0 21.89 0 0.624 6.454 98.4 1.8498 4 437.0 21.2 394.08 14.59 17.1
140 0.2498 0.0 21.89 0 0.624 5.857 98.2 1.6686 4 437.0 21.2 392.04 21.32 13.3
141 0.54452 0.0 21.89 0 0.624 6.151 97.9 1.6687 4 437.0 21.2 396.9 18.46 17.8
142 0.2909 0.0 21.89 0 0.624 6.174 93.6 1.6119 4 437.0 21.2 388.08 24.16 14.0
143 1.6286399999999999 0.0 21.89 0 0.624 5.019 100.0 1.4394 4 437.0 21.2 396.9 34.41 14.4
144 3.32105 0.0 19.58 1 0.871 5.403 100.0 1.3216 5 403.0 14.7 396.9 26.82 13.4
145 4.0974 0.0 19.58 0 0.871 5.468 100.0 1.4118 5 403.0 14.7 396.9 26.42 15.6
146 2.7797400000000003 0.0 19.58 0 0.871 4.903 97.8 1.3459 5 403.0 14.7 396.9 29.29 11.8
147 2.37934 0.0 19.58 0 0.871 6.13 100.0 1.4191 5 403.0 14.7 172.91 27.8 13.8
148 2.15505 0.0 19.58 0 0.871 5.628 100.0 1.5166 5 403.0 14.7 169.27 16.65 15.6
149 2.36862 0.0 19.58 0 0.871 4.926 95.7 1.4608 5 403.0 14.7 391.71 29.53 14.6
150 2.3309900000000003 0.0 19.58 0 0.871 5.186 93.8 1.5296 5 403.0 14.7 356.99 28.32 17.8
151 2.7339700000000002 0.0 19.58 0 0.871 5.597 94.9 1.5257 5 403.0 14.7 351.85 21.45 15.4
152 1.6566 0.0 19.58 0 0.871 6.122 97.3 1.618 5 403.0 14.7 372.8 14.1 21.5
153 1.49632 0.0 19.58 0 0.871 5.404 100.0 1.5916 5 403.0 14.7 341.6 13.28 19.6
154 1.12658 0.0 19.58 1 0.871 5.012 88.0 1.6102 5 403.0 14.7 343.28 12.12 15.3
155 2.14918 0.0 19.58 0 0.871 5.709 98.5 1.6232 5 403.0 14.7 261.95 15.79 19.4
156 1.41385 0.0 19.58 1 0.871 6.129 96.0 1.7494 5 403.0 14.7 321.02 15.12 17.0
157 3.5350099999999998 0.0 19.58 1 0.871 6.152 82.6 1.7455 5 403.0 14.7 88.01 15.02 15.6
158 2.4466799999999997 0.0 19.58 0 0.871 5.272 94.0 1.7364 5 403.0 14.7 88.63 16.14 13.1
159 1.22358 0.0 19.58 0 0.605 6.943 97.4 1.8773 5 403.0 14.7 363.43 4.59 41.3
160 1.34284 0.0 19.58 0 0.605 6.066 100.0 1.7573 5 403.0 14.7 353.89 6.43 24.3
161 1.4250200000000002 0.0 19.58 0 0.871 6.51 100.0 1.7659 5 403.0 14.7 364.31 7.39 23.3
162 1.27346 0.0 19.58 1 0.605 6.25 92.6 1.7984 5 403.0 14.7 338.92 5.5 27.0
163 1.46336 0.0 19.58 0 0.605 7.489 90.8 1.9709 5 403.0 14.7 374.43 1.73 50.0
164 1.8337700000000001 0.0 19.58 1 0.605 7.802 98.2 2.0407 5 403.0 14.7 389.61 1.92 50.0
165 1.51902 0.0 19.58 1 0.605 8.375 93.9 2.162 5 403.0 14.7 388.45 3.32 50.0
166 2.2423599999999997 0.0 19.58 0 0.605 5.854 91.8 2.422 5 403.0 14.7 395.11 11.64 22.7
167 2.924 0.0 19.58 0 0.605 6.101 93.0 2.2834 5 403.0 14.7 240.16 9.81 25.0
168 2.01019 0.0 19.58 0 0.605 7.929 96.2 2.0459 5 403.0 14.7 369.3 3.7 50.0
169 1.8002799999999999 0.0 19.58 0 0.605 5.877 79.2 2.4259 5 403.0 14.7 227.61 12.14 23.8
170 2.3004 0.0 19.58 0 0.605 6.319 96.1 2.1 5 403.0 14.7 297.09 11.1 23.8
171 2.4495299999999998 0.0 19.58 0 0.605 6.402 95.2 2.2625 5 403.0 14.7 330.04 11.32 22.3
172 1.2074200000000002 0.0 19.58 0 0.605 5.875 94.6 2.4259 5 403.0 14.7 292.29 14.43 17.4
173 2.3139 0.0 19.58 0 0.605 5.88 97.3 2.3887 5 403.0 14.7 348.13 12.03 19.1
174 0.13914 0.0 4.05 0 0.51 5.572 88.5 2.5961 5 296.0 16.6 396.9 14.69 23.1
175 0.09178 0.0 4.05 0 0.51 6.416 84.1 2.6463 5 296.0 16.6 395.5 9.04 23.6
176 0.08447 0.0 4.05 0 0.51 5.859 68.7 2.7019 5 296.0 16.6 393.23 9.64 22.6
177 0.06663999999999999 0.0 4.05 0 0.51 6.546 33.1 3.1323 5 296.0 16.6 390.96 5.33 29.4
178 0.07022 0.0 4.05 0 0.51 6.02 47.2 3.5549 5 296.0 16.6 393.23 10.11 23.2
179 0.05425 0.0 4.05 0 0.51 6.315 73.4 3.3175 5 296.0 16.6 395.6 6.29 24.6
180 0.06642 0.0 4.05 0 0.51 6.86 74.4 2.9153 5 296.0 16.6 391.27 6.92 29.9
181 0.0578 0.0 2.46 0 0.488 6.98 58.4 2.829 3 193.0 17.8 396.9 5.04 37.2
182 0.06588 0.0 2.46 0 0.488 7.765 83.3 2.741 3 193.0 17.8 395.56 7.56 39.8
183 0.06888 0.0 2.46 0 0.488 6.144 62.2 2.5979 3 193.0 17.8 396.9 9.45 36.2
184 0.09103 0.0 2.46 0 0.488 7.155 92.2 2.7006 3 193.0 17.8 394.12 4.82 37.9
185 0.10008 0.0 2.46 0 0.488 6.563 95.6 2.847 3 193.0 17.8 396.9 5.68 32.5
186 0.08308 0.0 2.46 0 0.488 5.604 89.8 2.9879 3 193.0 17.8 391.0 13.98 26.4
187 0.06047 0.0 2.46 0 0.488 6.153 68.8 3.2797 3 193.0 17.8 387.11 13.15 29.6
188 0.05602000000000001 0.0 2.46 0 0.488 7.831 53.6 3.1992 3 193.0 17.8 392.63 4.45 50.0
189 0.07875 45.0 3.44 0 0.437 6.782 41.1 3.7886 5 398.0 15.2 393.87 6.68 32.0
190 0.12579 45.0 3.44 0 0.437 6.556 29.1 4.5667 5 398.0 15.2 382.84 4.56 29.8
191 0.0837 45.0 3.44 0 0.437 7.185 38.9 4.5667 5 398.0 15.2 396.9 5.39 34.9
192 0.09068 45.0 3.44 0 0.437 6.951 21.5 6.4798 5 398.0 15.2 377.68 5.1 37.0
193 0.06911 45.0 3.44 0 0.437 6.739 30.8 6.4798 5 398.0 15.2 389.71 4.69 30.5
194 0.08664 45.0 3.44 0 0.437 7.178 26.3 6.4798 5 398.0 15.2 390.49 2.87 36.4
195 0.02187 60.0 2.93 0 0.401 6.8 9.9 6.2196 1 265.0 15.6 393.37 5.03 31.1
196 0.01439 60.0 2.93 0 0.401 6.604 18.8 6.2196 1 265.0 15.6 376.7 4.38 29.1
197 0.01381 80.0 0.46 0 0.422 7.875 32.0 5.6484 4 255.0 14.4 394.23 2.97 50.0
198 0.04011 80.0 1.52 0 0.404 7.287 34.1 7.309 2 329.0 12.6 396.9 4.08 33.3
199 0.04666 80.0 1.52 0 0.404 7.107 36.6 7.309 2 329.0 12.6 354.31 8.61 30.3
200 0.03768 80.0 1.52 0 0.404 7.274 38.3 7.309 2 329.0 12.6 392.2 6.62 34.6
201 0.0315 95.0 1.47 0 0.403 6.975 15.3 7.6534 3 402.0 17.0 396.9 4.56 34.9
202 0.01778 95.0 1.47 0 0.403 7.135 13.9 7.6534 3 402.0 17.0 384.3 4.45 32.9
203 0.03445 82.5 2.03 0 0.415 6.162 38.4 6.27 2 348.0 14.7 393.77 7.43 24.1
204 0.021769999999999998 82.5 2.03 0 0.415 7.61 15.7 6.27 2 348.0 14.7 395.38 3.11 42.3
205 0.0351 95.0 2.68 0 0.4161 7.853 33.2 5.118 4 224.0 14.7 392.78 3.81 48.5
206 0.02009 95.0 2.68 0 0.4161 8.034 31.9 5.118 4 224.0 14.7 390.55 2.88 50.0
207 0.13642 0.0 10.59 0 0.489 5.891 22.3 3.9454 4 277.0 18.6 396.9 10.87 22.6
208 0.22969 0.0 10.59 0 0.489 6.326 52.5 4.3549 4 277.0 18.6 394.87 10.97 24.4
209 0.25199 0.0 10.59 0 0.489 5.783 72.7 4.3549 4 277.0 18.6 389.43 18.06 22.5
210 0.13587 0.0 10.59 1 0.489 6.064 59.1 4.2392 4 277.0 18.6 381.32 14.66 24.4
211 0.43571000000000004 0.0 10.59 1 0.489 5.344 100.0 3.875 4 277.0 18.6 396.9 23.09 20.0
212 0.17446 0.0 10.59 1 0.489 5.96 92.1 3.8771 4 277.0 18.6 393.25 17.27 21.7
213 0.37578 0.0 10.59 1 0.489 5.404 88.6 3.665 4 277.0 18.6 395.24 23.98 19.3
214 0.21719000000000002 0.0 10.59 1 0.489 5.807 53.8 3.6526 4 277.0 18.6 390.94 16.03 22.4
215 0.14052 0.0 10.59 0 0.489 6.375 32.3 3.9454 4 277.0 18.6 385.81 9.38 28.1
216 0.28955 0.0 10.59 0 0.489 5.412 9.8 3.5875 4 277.0 18.6 348.93 29.55 23.7
217 0.19802 0.0 10.59 0 0.489 6.182 42.4 3.9454 4 277.0 18.6 393.63 9.47 25.0
218 0.0456 0.0 13.89 1 0.55 5.888 56.0 3.1121 5 276.0 16.4 392.8 13.51 23.3
219 0.07013 0.0 13.89 0 0.55 6.642 85.1 3.4211 5 276.0 16.4 392.78 9.69 28.7
220 0.11069000000000001 0.0 13.89 1 0.55 5.951 93.8 2.8893 5 276.0 16.4 396.9 17.92 21.5
221 0.11425 0.0 13.89 1 0.55 6.373 92.4 3.3633 5 276.0 16.4 393.74 10.5 23.0
222 0.35809 0.0 6.2 1 0.507 6.951 88.5 2.8617 8 307.0 17.4 391.7 9.71 26.7
223 0.40771 0.0 6.2 1 0.507 6.164 91.3 3.048 8 307.0 17.4 395.24 21.46 21.7
224 0.62356 0.0 6.2 1 0.507 6.879 77.7 3.2721 8 307.0 17.4 390.39 9.93 27.5
225 0.6147 0.0 6.2 0 0.507 6.618 80.8 3.2721 8 307.0 17.4 396.9 7.6 30.1
226 0.31533 0.0 6.2 0 0.504 8.266 78.3 2.8944 8 307.0 17.4 385.05 4.14 44.8
227 0.52693 0.0 6.2 0 0.504 8.725 83.0 2.8944 8 307.0 17.4 382.0 4.63 50.0
228 0.38214000000000004 0.0 6.2 0 0.504 8.04 86.5 3.2157 8 307.0 17.4 387.38 3.13 37.6
229 0.41238 0.0 6.2 0 0.504 7.163 79.9 3.2157 8 307.0 17.4 372.08 6.36 31.6
230 0.29819 0.0 6.2 0 0.504 7.686 17.0 3.3751 8 307.0 17.4 377.51 3.92 46.7
231 0.44178 0.0 6.2 0 0.504 6.552 21.4 3.3751 8 307.0 17.4 380.34 3.76 31.5
232 0.537 0.0 6.2 0 0.504 5.981 68.1 3.6715 8 307.0 17.4 378.35 11.65 24.3
233 0.46296000000000004 0.0 6.2 0 0.504 7.412 76.9 3.6715 8 307.0 17.4 376.14 5.25 31.7
234 0.57529 0.0 6.2 0 0.507 8.337 73.3 3.8384 8 307.0 17.4 385.91 2.47 41.7
235 0.33147 0.0 6.2 0 0.507 8.247 70.4 3.6519 8 307.0 17.4 378.95 3.95 48.3
236 0.44791000000000003 0.0 6.2 1 0.507 6.726 66.5 3.6519 8 307.0 17.4 360.2 8.05 29.0
237 0.33045 0.0 6.2 0 0.507 6.086 61.5 3.6519 8 307.0 17.4 376.75 10.88 24.0
238 0.52058 0.0 6.2 1 0.507 6.631 76.5 4.148 8 307.0 17.4 388.45 9.54 25.1
239 0.51183 0.0 6.2 0 0.507 7.358 71.6 4.148 8 307.0 17.4 390.07 4.73 31.5
240 0.08244 30.0 4.93 0 0.428 6.481 18.5 6.1899 6 300.0 16.6 379.41 6.36 23.7
241 0.09252 30.0 4.93 0 0.428 6.606 42.2 6.1899 6 300.0 16.6 383.78 7.37 23.3
242 0.11329000000000002 30.0 4.93 0 0.428 6.897 54.3 6.3361 6 300.0 16.6 391.25 11.38 22.0
243 0.10612 30.0 4.93 0 0.428 6.095 65.1 6.3361 6 300.0 16.6 394.62 12.4 20.1
244 0.1029 30.0 4.93 0 0.428 6.358 52.9 7.0355 6 300.0 16.6 372.75 11.22 22.2
245 0.12757000000000002 30.0 4.93 0 0.428 6.393 7.8 7.0355 6 300.0 16.6 374.71 5.19 23.7
246 0.20608 22.0 5.86 0 0.431 5.593 76.5 7.9549 7 330.0 19.1 372.49 12.5 17.6
247 0.19133 22.0 5.86 0 0.431 5.605 70.2 7.9549 7 330.0 19.1 389.13 18.46 18.5
248 0.33983 22.0 5.86 0 0.431 6.108 34.9 8.0555 7 330.0 19.1 390.18 9.16 24.3
249 0.19657 22.0 5.86 0 0.431 6.226 79.2 8.0555 7 330.0 19.1 376.14 10.15 20.5
250 0.16439 22.0 5.86 0 0.431 6.433 49.1 7.8265 7 330.0 19.1 374.71 9.52 24.5
251 0.19072999999999998 22.0 5.86 0 0.431 6.718 17.5 7.8265 7 330.0 19.1 393.74 6.56 26.2
252 0.1403 22.0 5.86 0 0.431 6.487 13.0 7.3967 7 330.0 19.1 396.28 5.9 24.4
253 0.21409 22.0 5.86 0 0.431 6.438 8.9 7.3967 7 330.0 19.1 377.07 3.59 24.8
254 0.08221 22.0 5.86 0 0.431 6.957 6.8 8.9067 7 330.0 19.1 386.09 3.53 29.6
255 0.36894 22.0 5.86 0 0.431 8.259 8.4 8.9067 7 330.0 19.1 396.9 3.54 42.8
256 0.04819 80.0 3.64 0 0.392 6.108 32.0 9.2203 1 315.0 16.4 392.89 6.57 21.9
257 0.035480000000000005 80.0 3.64 0 0.392 5.876 19.1 9.2203 1 315.0 16.4 395.18 9.25 20.9
258 0.015380000000000001 90.0 3.75 0 0.394 7.454 34.2 6.3361 3 244.0 15.9 386.34 3.11 44.0
259 0.61154 20.0 3.97 0 0.647 8.704 86.9 1.801 5 264.0 13.0 389.7 5.12 50.0
260 0.66351 20.0 3.97 0 0.647 7.333 100.0 1.8946 5 264.0 13.0 383.29 7.79 36.0
261 0.65665 20.0 3.97 0 0.647 6.842 100.0 2.0107 5 264.0 13.0 391.93 6.9 30.1
262 0.5401100000000001 20.0 3.97 0 0.647 7.203 81.8 2.1121 5 264.0 13.0 392.8 9.59 33.8
263 0.5341199999999999 20.0 3.97 0 0.647 7.52 89.4 2.1398 5 264.0 13.0 388.37 7.26 43.1
264 0.5201399999999999 20.0 3.97 0 0.647 8.398 91.5 2.2885 5 264.0 13.0 386.86 5.91 48.8
265 0.82526 20.0 3.97 0 0.647 7.327 94.5 2.0788 5 264.0 13.0 393.42 11.25 31.0
266 0.55007 20.0 3.97 0 0.647 7.206 91.6 1.9301 5 264.0 13.0 387.89 8.1 36.5
267 0.76162 20.0 3.97 0 0.647 5.56 62.8 1.9865 5 264.0 13.0 392.4 10.45 22.8
268 0.7857 20.0 3.97 0 0.647 7.014 84.6 2.1329 5 264.0 13.0 384.07 14.79 30.7
269 0.57834 20.0 3.97 0 0.575 8.297 67.0 2.4216 5 264.0 13.0 384.54 7.44 50.0
270 0.5405 20.0 3.97 0 0.575 7.47 52.6 2.872 5 264.0 13.0 390.3 3.16 43.5
271 0.09065 20.0 6.96 1 0.464 5.92 61.5 3.9175 3 223.0 18.6 391.34 13.65 20.7
272 0.29916 20.0 6.96 0 0.464 5.856 42.1 4.429 3 223.0 18.6 388.65 13.0 21.1
273 0.16211 20.0 6.96 0 0.464 6.24 16.3 4.429 3 223.0 18.6 396.9 6.59 25.2
274 0.1146 20.0 6.96 0 0.464 6.538 58.7 3.9175 3 223.0 18.6 394.96 7.73 24.4
275 0.22188000000000002 20.0 6.96 1 0.464 7.691 51.8 4.3665 3 223.0 18.6 390.77 6.58 35.2
276 0.05644 40.0 6.41 1 0.447 6.758 32.9 4.0776 4 254.0 17.6 396.9 3.53 32.4
277 0.09604 40.0 6.41 0 0.447 6.854 42.8 4.2673 4 254.0 17.6 396.9 2.98 32.0
278 0.10469 40.0 6.41 1 0.447 7.267 49.0 4.7872 4 254.0 17.6 389.25 6.05 33.2
279 0.061270000000000005 40.0 6.41 1 0.447 6.826 27.6 4.8628 4 254.0 17.6 393.45 4.16 33.1
280 0.07977999999999999 40.0 6.41 0 0.447 6.482 32.1 4.1403 4 254.0 17.6 396.9 7.19 29.1
281 0.21038 20.0 3.33 0 0.4429 6.812 32.2 4.1007 5 216.0 14.9 396.9 4.85 35.1
282 0.03578 20.0 3.33 0 0.4429 7.82 64.5 4.6947 5 216.0 14.9 387.31 3.76 45.4
283 0.03705 20.0 3.33 0 0.4429 6.968 37.2 5.2447 5 216.0 14.9 392.23 4.59 35.4
284 0.06129 20.0 3.33 1 0.4429 7.645 49.7 5.2119 5 216.0 14.9 377.07 3.01 46.0
285 0.015009999999999999 90.0 1.21 1 0.401 7.923 24.8 5.885 1 198.0 13.6 395.52 3.16 50.0
286 0.009059999999999999 90.0 2.97 0 0.4 7.088 20.8 7.3073 1 285.0 15.3 394.72 7.85 32.2
287 0.01096 55.0 2.25 0 0.389 6.453 31.9 7.3073 1 300.0 15.3 394.72 8.23 22.0
288 0.01965 80.0 1.76 0 0.385 6.23 31.5 9.0892 1 241.0 18.2 341.6 12.93 20.1
289 0.03871 52.5 5.32 0 0.405 6.209 31.3 7.3172 6 293.0 16.6 396.9 7.14 23.2
290 0.0459 52.5 5.32 0 0.405 6.315 45.6 7.3172 6 293.0 16.6 396.9 7.6 22.3
291 0.04297 52.5 5.32 0 0.405 6.565 22.9 7.3172 6 293.0 16.6 371.72 9.51 24.8
292 0.035019999999999996 80.0 4.95 0 0.411 6.861 27.9 5.1167 4 245.0 19.2 396.9 3.33 28.5
293 0.07886 80.0 4.95 0 0.411 7.148 27.7 5.1167 4 245.0 19.2 396.9 3.56 37.3
294 0.03615 80.0 4.95 0 0.411 6.63 23.4 5.1167 4 245.0 19.2 396.9 4.7 27.9
295 0.08265 0.0 13.92 0 0.437 6.127 18.4 5.5027 4 289.0 16.0 396.9 8.58 23.9
296 0.08199 0.0 13.92 0 0.437 6.009 42.3 5.5027 4 289.0 16.0 396.9 10.4 21.7
297 0.12932000000000002 0.0 13.92 0 0.437 6.678 31.1 5.9604 4 289.0 16.0 396.9 6.27 28.6
298 0.053720000000000004 0.0 13.92 0 0.437 6.549 51.0 5.9604 4 289.0 16.0 392.85 7.39 27.1
299 0.14103 0.0 13.92 0 0.437 5.79 58.0 6.32 4 289.0 16.0 396.9 15.84 20.3
300 0.06466000000000001 70.0 2.24 0 0.4 6.345 20.1 7.8278 5 358.0 14.8 368.24 4.97 22.5
301 0.05561 70.0 2.24 0 0.4 7.041 10.0 7.8278 5 358.0 14.8 371.58 4.74 29.0
302 0.04417 70.0 2.24 0 0.4 6.871 47.4 7.8278 5 358.0 14.8 390.86 6.07 24.8
303 0.03537 34.0 6.09 0 0.433 6.59 40.4 5.4917 7 329.0 16.1 395.75 9.5 22.0
304 0.09266 34.0 6.09 0 0.433 6.495 18.4 5.4917 7 329.0 16.1 383.61 8.67 26.4
305 0.1 34.0 6.09 0 0.433 6.982 17.7 5.4917 7 329.0 16.1 390.43 4.86 33.1
306 0.05515 33.0 2.18 0 0.472 7.236 41.1 4.022 7 222.0 18.4 393.68 6.93 36.1
307 0.05479 33.0 2.18 0 0.472 6.616 58.1 3.37 7 222.0 18.4 393.36 8.93 28.4
308 0.07503 33.0 2.18 0 0.472 7.42 71.9 3.0992 7 222.0 18.4 396.9 6.47 33.4
309 0.049319999999999996 33.0 2.18 0 0.472 6.849 70.3 3.1827 7 222.0 18.4 396.9 7.53 28.2
310 0.49298000000000003 0.0 9.9 0 0.544 6.635 82.5 3.3175 4 304.0 18.4 396.9 4.54 22.8
311 0.3494 0.0 9.9 0 0.544 5.972 76.7 3.1025 4 304.0 18.4 396.24 9.97 20.3
312 2.63548 0.0 9.9 0 0.544 4.973 37.8 2.5194 4 304.0 18.4 350.45 12.64 16.1
313 0.7904100000000001 0.0 9.9 0 0.544 6.122 52.8 2.6403 4 304.0 18.4 396.9 5.98 22.1
314 0.26169000000000003 0.0 9.9 0 0.544 6.023 90.4 2.834 4 304.0 18.4 396.3 11.72 19.4
315 0.26938 0.0 9.9 0 0.544 6.266 82.8 3.2628 4 304.0 18.4 393.39 7.9 21.6
316 0.3692 0.0 9.9 0 0.544 6.567 87.3 3.6023 4 304.0 18.4 395.69 9.28 23.8
317 0.25356 0.0 9.9 0 0.544 5.705 77.7 3.945 4 304.0 18.4 396.42 11.5 16.2
318 0.31827 0.0 9.9 0 0.544 5.914 83.2 3.9986 4 304.0 18.4 390.7 18.33 17.8
319 0.24522 0.0 9.9 0 0.544 5.782 71.7 4.0317 4 304.0 18.4 396.9 15.94 19.8
320 0.40202 0.0 9.9 0 0.544 6.382 67.2 3.5325 4 304.0 18.4 395.21 10.36 23.1
321 0.47547 0.0 9.9 0 0.544 6.113 58.8 4.0019 4 304.0 18.4 396.23 12.73 21.0
322 0.1676 0.0 7.38 0 0.493 6.426 52.3 4.5404 5 287.0 19.6 396.9 7.2 23.8
323 0.18159 0.0 7.38 0 0.493 6.376 54.3 4.5404 5 287.0 19.6 396.9 6.87 23.1
324 0.35114 0.0 7.38 0 0.493 6.041 49.9 4.7211 5 287.0 19.6 396.9 7.7 20.4
325 0.28392 0.0 7.38 0 0.493 5.708 74.3 4.7211 5 287.0 19.6 391.13 11.74 18.5
326 0.34109 0.0 7.38 0 0.493 6.415 40.1 4.7211 5 287.0 19.6 396.9 6.12 25.0
327 0.19186 0.0 7.38 0 0.493 6.431 14.7 5.4159 5 287.0 19.6 393.68 5.08 24.6
328 0.30346999999999996 0.0 7.38 0 0.493 6.312 28.9 5.4159 5 287.0 19.6 396.9 6.15 23.0
329 0.24103000000000002 0.0 7.38 0 0.493 6.083 43.7 5.4159 5 287.0 19.6 396.9 12.79 22.2
330 0.06617 0.0 3.24 0 0.46 5.868 25.8 5.2146 4 430.0 16.9 382.44 9.97 19.3
331 0.06724 0.0 3.24 0 0.46 6.333 17.2 5.2146 4 430.0 16.9 375.21 7.34 22.6
332 0.045439999999999994 0.0 3.24 0 0.46 6.144 32.2 5.8736 4 430.0 16.9 368.57 9.09 19.8
333 0.050230000000000004 35.0 6.06 0 0.4379 5.706 28.4 6.6407 1 304.0 16.9 394.02 12.43 17.1
334 0.03466 35.0 6.06 0 0.4379 6.031 23.3 6.6407 1 304.0 16.9 362.25 7.83 19.4
335 0.05083 0.0 5.19 0 0.515 6.316 38.1 6.4584 5 224.0 20.2 389.71 5.68 22.2
336 0.037380000000000004 0.0 5.19 0 0.515 6.31 38.5 6.4584 5 224.0 20.2 389.4 6.75 20.7
337 0.03961 0.0 5.19 0 0.515 6.037 34.5 5.9853 5 224.0 20.2 396.9 8.01 21.1
338 0.03427 0.0 5.19 0 0.515 5.869 46.3 5.2311 5 224.0 20.2 396.9 9.8 19.5
339 0.030410000000000003 0.0 5.19 0 0.515 5.895 59.6 5.615 5 224.0 20.2 394.81 10.56 18.5
340 0.03306 0.0 5.19 0 0.515 6.059 37.3 4.8122 5 224.0 20.2 396.14 8.51 20.6
341 0.054970000000000005 0.0 5.19 0 0.515 5.985 45.4 4.8122 5 224.0 20.2 396.9 9.74 19.0
342 0.06151 0.0 5.19 0 0.515 5.968 58.5 4.8122 5 224.0 20.2 396.9 9.29 18.7
343 0.013009999999999999 35.0 1.52 0 0.442 7.241 49.3 7.0379 1 284.0 15.5 394.74 5.49 32.7
344 0.024980000000000002 0.0 1.89 0 0.518 6.54 59.7 6.2669 1 422.0 15.9 389.96 8.65 16.5
345 0.02543 55.0 3.78 0 0.484 6.696 56.4 5.7321 5 370.0 17.6 396.9 7.18 23.9
346 0.030489999999999996 55.0 3.78 0 0.484 6.874 28.1 6.4654 5 370.0 17.6 387.97 4.61 31.2
347 0.03113 0.0 4.39 0 0.442 6.014 48.5 8.0136 3 352.0 18.8 385.64 10.53 17.5
348 0.06162 0.0 4.39 0 0.442 5.898 52.3 8.0136 3 352.0 18.8 364.61 12.67 17.2
349 0.0187 85.0 4.15 0 0.429 6.516 27.7 8.5353 4 351.0 17.9 392.43 6.36 23.1
350 0.015009999999999999 80.0 2.01 0 0.435 6.635 29.7 8.344 4 280.0 17.0 390.94 5.99 24.5
351 0.02899 40.0 1.25 0 0.429 6.939 34.5 8.7921 1 335.0 19.7 389.85 5.89 26.6
352 0.062110000000000005 40.0 1.25 0 0.429 6.49 44.4 8.7921 1 335.0 19.7 396.9 5.98 22.9
353 0.0795 60.0 1.69 0 0.411 6.579 35.9 10.7103 4 411.0 18.3 370.78 5.49 24.1
354 0.07244 60.0 1.69 0 0.411 5.884 18.5 10.7103 4 411.0 18.3 392.33 7.79 18.6
355 0.01709 90.0 2.02 0 0.41 6.728 36.1 12.1265 5 187.0 17.0 384.46 4.5 30.1
356 0.04301 80.0 1.91 0 0.413 5.663 21.9 10.5857 4 334.0 22.0 382.8 8.05 18.2
357 0.10659 80.0 1.91 0 0.413 5.936 19.5 10.5857 4 334.0 22.0 376.04 5.57 20.6
358 8.98296 0.0 18.1 1 0.77 6.212 97.4 2.1222 24 666.0 20.2 377.73 17.6 17.8
359 3.8497 0.0 18.1 1 0.77 6.395 91.0 2.5052 24 666.0 20.2 391.34 13.27 21.7
360 5.20177 0.0 18.1 1 0.77 6.127 83.4 2.7227 24 666.0 20.2 395.43 11.48 22.7
361 4.26131 0.0 18.1 0 0.77 6.112 81.3 2.5091 24 666.0 20.2 390.74 12.67 22.6
362 4.541919999999999 0.0 18.1 0 0.77 6.398 88.0 2.5182 24 666.0 20.2 374.56 7.79 25.0
363 3.83684 0.0 18.1 0 0.77 6.251 91.1 2.2955 24 666.0 20.2 350.65 14.19 19.9
364 3.6782199999999996 0.0 18.1 0 0.77 5.362 96.2 2.1036 24 666.0 20.2 380.79 10.19 20.8
365 4.22239 0.0 18.1 1 0.77 5.803 89.0 1.9047 24 666.0 20.2 353.04 14.64 16.8
366 3.4742800000000003 0.0 18.1 1 0.718 8.78 82.9 1.9047 24 666.0 20.2 354.55 5.29 21.9
367 4.55587 0.0 18.1 0 0.718 3.561 87.9 1.6132 24 666.0 20.2 354.7 7.12 27.5
368 3.69695 0.0 18.1 0 0.718 4.963 91.4 1.7523 24 666.0 20.2 316.03 14.0 21.9
369 13.5222 0.0 18.1 0 0.631 3.863 100.0 1.5106 24 666.0 20.2 131.42 13.33 23.1
370 4.898219999999999 0.0 18.1 0 0.631 4.97 100.0 1.3325 24 666.0 20.2 375.52 3.26 50.0
371 5.669980000000001 0.0 18.1 1 0.631 6.683 96.8 1.3567 24 666.0 20.2 375.33 3.73 50.0
372 6.53876 0.0 18.1 1 0.631 7.016 97.5 1.2024 24 666.0 20.2 392.05 2.96 50.0
373 9.2323 0.0 18.1 0 0.631 6.216 100.0 1.1691 24 666.0 20.2 366.15 9.53 50.0
374 8.26725 0.0 18.1 1 0.668 5.875 89.6 1.1296 24 666.0 20.2 347.88 8.88 50.0
375 11.1081 0.0 18.1 0 0.668 4.906 100.0 1.1742 24 666.0 20.2 396.9 34.77 13.8
376 18.4982 0.0 18.1 0 0.668 4.138 100.0 1.137 24 666.0 20.2 396.9 37.97 13.8
377 19.6091 0.0 18.1 0 0.671 7.313 97.9 1.3163 24 666.0 20.2 396.9 13.44 15.0
378 15.288 0.0 18.1 0 0.671 6.649 93.3 1.3449 24 666.0 20.2 363.02 23.24 13.9
379 9.82349 0.0 18.1 0 0.671 6.794 98.8 1.358 24 666.0 20.2 396.9 21.24 13.3
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## 简介
## 贡献者信息
本开源内容由张晋、杨佳达、牧小熊、杨杨卓然、姚昱君 组织整理。
将于2021年08月07日进行组队学习我们还在进行最后的校对近期会提交上来。
| 姓名 | 介绍 | 个人主页 |
| ------ | ------------------------------- | ------------------------------- |
| 张晋 | Datawhale成员算法竞赛爱好者 | https://blog.csdn.net/weixin_44585839/ |
| 杨佳达 | 数据挖掘师Datawhale成员目前在国内某第三方数据服务公司做数据分析挖掘及数据产品 | https://github.com/yangjiada |
| 牧小熊 | 华中农业大学研究生Datawhale成员Datawhale优秀原创作者 | https://www.zhihu.com/people/muxiaoxiong |
| 杨杨卓然 | 英俊潇洒富得流油的统计博士 | https://yangzhuoranyang.com |
| 姚昱君 | 悉尼大学Datawhale成员 | https://blog.csdn.net/Yao_June |
## 课程简介
- 课程设计成员:**张晋**、杨佳达、牧小熊、杨杨卓然、姚昱君
- 学习周期11天每天平均花费时间1小时-3小时不等根据个人学习接受能力强弱有所浮动。
- 学习形式:理论学习 + 练习
- 人群定位对数据科学有基本了解希望学习R语言的同学。
- 先修内容:无
- 难度系数:⭐⭐
## 课程大纲
**Task00熟悉规则与R语言入门1天**【 [预览](https://rpubs.com/June_Yao/task00_introduction) 】
- 组队、修改群昵称。
- 熟悉打卡规则。
- 安装
- 环境配置
**Task01 数据结构与数据集 2天**【 [预览](https://rpubs.com/June_Yao/task01_data_structure) 】
- 编码基础
- 数据类型
- 特殊数据类型
- table like 数据类型
- 加载数据 (csv, rds, excel, Rdata)
- 实例
**Task02 数据清洗与准备 2天**【 [预览](https://rpubs.com/June_Yao/task02_data_preparation) 】
- 重复值处理
- 缺失值识别与处理
- 异常值识别与处理
- 特征处理
- 规范化与偏态数据
**Task03 基本统计分析 2天**【 [预览](https://rpubs.com/June_Yao/task03_statistics) 】
- 多种方法获取描述性统计量
- 分组计算描述性统计
- 频数表和列联表
- 相关
- 方差分析
**Task04 数据可视化2天**【 [预览](https://rpubs.com/June_Yao/task04_visualization) 】
- ggplot2包介绍
- 散点图
- 直方图
- 柱状图
- 饼状图
- 折线图
- ggplot2扩展包主题
**Task05 模型2天**【 [预览](https://rpubs.com/June_Yao/task05_model) 】
- 回归模型
- 分类模型
关于Datawhale Datawhale是一个专注于数据科学与AI领域的开源组织汇集了众多领域院校和知名企业的优秀学习者聚合了一群有开源精神和探索精神的团队成员。Datawhale 以“for the learner和学习者一起成长”为愿景鼓励真实地展现自我、开放包容、互信互助、敢于试错和勇于担当。同时 Datawhale 用开源的理念去探索开源内容、开源学习和开源方案,赋能人才培养,助力人才成长,建立起人与人,人与知识,人与企业和人与未来的联结。 本次数据挖掘路径学习专题知识将在天池分享详情可关注Datawhale
![logo.png](https://camo.githubusercontent.com/8578ee173c78b587d5058439bbd0b98fa39c173def229a8c3d957e62aac0b649/68747470733a2f2f696d672d626c6f672e6373646e696d672e636e2f323032303039313330313032323639382e706e67237069635f63656e746572)