Homework6

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

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)

ggplot(texas_data,aes(x=x,y=y)) + geom_point() + geom_smooth(method='lm',color='red')

## `geom_smooth()` using formula = 'y ~ x'

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

summary(poverty_model)

## 
## Call:
## lm(formula = x ~ y, data = texas_data)
## 
## Residuals:
##         1         2         3         4         5         6         7 
##  0.008651 -0.005788 -0.014070  0.012367  0.058902 -0.022055 -0.038008 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.458385   0.086014   5.329  0.00312 **
## y           -0.007022   0.002145  -3.274  0.02211 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03423 on 5 degrees of freedom
## Multiple R-squared:  0.6819, Adjusted R-squared:  0.6183 
## F-statistic: 10.72 on 1 and 5 DF,  p-value: 0.02211

Poverty effects 95% of turnout dropping in the counties with 68% of x (poverty level) being explained by y (voter turnout). Y has a negative effect on X, reducing it with every increase.

plot(poverty_model,which=1)

No, while it is close to linearity, the final two points break it.