Homework 6

HOMEWORK

1. Load your chosen dataset into Rmarkdown
2. Select the dependent variable you are interested in, along with independent variables which you believe are causing the dependent variable

• My dependent variable is voter turnout throughout the country, my independent variables are felon ineligibility and will

3. create a linear model using the “lm()” command, save it to some object
4. call a “summary()” on your new model
5. interpret the model’s r-squared and p-values. How much of the dependent variable does the overall model explain? What are the significant variables? What are the insignificant variables?
6. Choose some significant independent variables. Interpret its Estimates (or Beta Coefficients). How do the independent variables individually affect the dependent variable?
7. Does the model you create meet or violate the assumption of linearity? Show your work with “plot(x,which=1)”

data1<-(X2020Election[-1,])

Elections <- read_xlsx("Quantitative Methods/2024Elections.xlsx")

## New names:
## • `` -> `...4`

Elections2024<- (Elections[-1,])
#removes United States total row 
Elections2024$INELIGIBLE_FELONS_TOTAL<- parse_number(Elections2024$INELIGIBLE_FELONS_TOTAL)
Elections2024$TOTAL_BALLOTS_COUNTED<- parse_number(Elections2024$TOTAL_BALLOTS_COUNTED)
Elections2024$VEP<- parse_number(Elections2024$VEP)
#Elections2024$INELIGIBLE_FELONS_TOTAL <- as.numeric(Elections2024$INELIGIBLE_FELONS_TOTAL)
#MutantElections2024<- Elections2024 %>% mutate(INELIGIBLE_FELONS_TOTAL) = as.numeric(INELIGIBLE_FELONS_TOTAL)

3. create a linear model using the “lm()” command, save it to some object

Election_model<-lm(TOTAL_BALLOTS_COUNTED~VEP + INELIGIBLE_FELONS_TOTAL, data=(Elections2024))
#Election_model<-lm(TOTAL_BALLOTS_COUNTED~VEP, data=(Elections2024))
#Election_model<-lm(TOTAL_BALLOTS_COUNTED~ INELIGIBLE_FELONS_TOTAL, data=(Elections2024))

4. call a “summary()” on your new model

summary(Election_model)

## 
## Call:
## lm(formula = TOTAL_BALLOTS_COUNTED ~ VEP + INELIGIBLE_FELONS_TOTAL, 
##     data = (Elections2024))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -637060 -134507  -77761   84991  793619 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              1.225e+05  6.184e+04   1.981  0.05336 .  
## VEP                      6.467e-01  1.156e-02  55.963  < 2e-16 ***
## INELIGIBLE_FELONS_TOTAL -2.176e+00  7.393e-01  -2.943  0.00499 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 321800 on 48 degrees of freedom
## Multiple R-squared:  0.9902, Adjusted R-squared:  0.9898 
## F-statistic:  2433 on 2 and 48 DF,  p-value: < 2.2e-16

5. interpret the model’s r-squared and p-values. How much of the dependent variable does the overall model explain? What are the significant variables? What are the insignificant variables?

First, the above information shows that there is a significant R-squared value which means the dependent variable is explained confidently by the independent variables used in the model. At 98.98% the model accounts for the variance in Total Ballots Counted. The P-Value’s being near zero means that there is a strong evidence that the predictors used are statistically significant. Both variables are significant, but VEP (Voter eligible population) has a more defined linear relationship with the dependent variable, and understandably so. As VEP falls, so do the number of ballots counted. I wouldn’t call ineligible voters insignificant, but compared to the VEP variable, it is significantly less reliable.

6. Choose some significant independent variables. Interpret its Estimates (or Beta Coefficients). How do the independent variables individually affect the dependent variable?

In VEP, for every one individual that is eligible to vote, we can estimate that Total Ballots Counted will increase by 6.467e-01 or .6467. For Ineligible Felon Total, the estimate has a negative relationship with Total Ballots Counted with an estimate of -2.176e+00 or -2.176 to Total Ballots Counted for every one Ineligible Felon Total.

7. Does the model you create meet or violate the assumption of linearity? Show your work with “plot(x,which=1)”

plot(Election_model,which=1)

This model violates the assumption of linearity as the red line shifts significantly midway through.