Homework7

library(tibble)
library(ggplot2)
library(readxl)
library(tidyverse)

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library(lmtest)

## Warning: package 'lmtest' was built under R version 4.4.2

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 4.4.2

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library(MASS)

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library(car)

## Loading required package: carData
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## Attaching package: 'car'
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read_excel("TexasCountyPoverty.xlsx")

## # A tibble: 7 × 4
##   `Label (Grouping)`   Population for whom …¹ pct_decimal county_vote_turnout …²
##   <chr>                                 <dbl>       <dbl>                  <dbl>
## 1 Bexar County, Texas…                  0.157       0.157                   44.2
## 2 Dallas County, Texa…                  0.142       0.142                   44.2
## 3 El Paso County, Tex…                  0.213       0.213                   32.9
## 4 Harris County, Texa…                  0.165       0.165                   43.5
## 5 Hidalgo County, Tex…                  0.276       0.276                   34.4
## 6 Tarrant County, Tex…                  0.106       0.106                   47.0
## 7 Webb County, Texas!…                  0.201       0.201                   31.2
## # ℹ abbreviated names: ¹​`Population for whom poverty status is determined`,
## #   ²​`county_vote_turnout ?`

TexasCountyPoverty <- read_excel("TexasCountyPoverty.xlsx")

x<-TexasCountyPoverty$`Population for whom poverty status is determined`
y<-TexasCountyPoverty$`county_vote_turnout ?`
texas_data<-data.frame(x=x,y=y)

TexasCountyPoverty <- read_excel("TexasCountyPoverty.xlsx")

poverty_model<-lm(x~y,data = texas_data)

raintest(poverty_model)

## 
##  Rainbow test
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## data:  poverty_model
## Rain = 0.28727, df1 = 4, df2 = 1, p-value = 0.8645

# Rainbow test shows that the model has high linearity

durbinWatsonTest(poverty_model)

##  lag Autocorrelation D-W Statistic p-value
##    1      0.02132838      1.698045   0.898
##  Alternative hypothesis: rho != 0

# errors are indpendent

bptest(poverty_model)

## 
##  studentized Breusch-Pagan test
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## data:  poverty_model
## BP = 2.1205, df = 1, p-value = 0.1453

# null hypothesis can be rejected

plot(poverty_model,which=2)

shapiro.test(poverty_model$residuals)

## 
##  Shapiro-Wilk normality test
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## data:  poverty_model$residuals
## W = 0.93508, p-value = 0.5949

# results may be normal

There are only two values so multicolinarity is not an issue.