Homework 7 - Alise Hunte

1. Load your preferred dataset into R studio

library(tidyverse)

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library(readxl)
library(lmtest)

## Loading required package: zoo
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## Attaching package: 'zoo'
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## The following objects are masked from 'package:base':
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##     as.Date, as.Date.numeric

library(MASS)

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## Attaching package: 'MASS'
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setwd("~/Desktop/UTSA/Quantitative Methods/RStudio")

district <- read_excel("district.xls")

clean_district<-district |> drop_na()

2. Create a linear model “lm()” from the variables, with a continuous dependent variable as the outcome

district_model<-lm(DA0GR21N~DPSTURNR+DPFRAALLK, data=clean_district)

3. Check the following assumptions:

1. Linearity (plot and raintest)

plot(district_model,which=1)

raintest(district_model)

## 
##  Rainbow test
## 
## data:  district_model
## Rain = 0.67354, df1 = 162, df2 = 158, p-value = 0.9936

2. Independence of errors (durbin-watson)

library(car)

## Loading required package: carData

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## Attaching package: 'car'

## The following object is masked from 'package:dplyr':
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durbinWatsonTest(district_model)

##  lag Autocorrelation D-W Statistic p-value
##    1       0.1361684      1.725153    0.03
##  Alternative hypothesis: rho != 0

3. Homoscedasticity (plot, bptest)

plot(district_model,which=3)

bptest(district_model)

## 
##  studentized Breusch-Pagan test
## 
## data:  district_model
## BP = 2.3293, df = 2, p-value = 0.312

4. Normality of residuals (QQ plot, shapiro test)

plot(district_model,which=2)

shapiro.test(district_model$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  district_model$residuals
## W = 0.67851, p-value < 2.2e-16

5. No multicolinarity (VIF, cor)

kitchen_sink<-lm(DA0GR21N~DPSTURNR+DPFRAALLK+DPSTTOSA+DPSAKIDR+DPSTKIDR+DPFVTOTK+DPFRAOPRT+DPFEAOPFT+DPFEAOPFK+DPFEAINSP,data=clean_district)


vif(kitchen_sink)

##   DPSTURNR  DPFRAALLK   DPSTTOSA   DPSAKIDR   DPSTKIDR   DPFVTOTK  DPFRAOPRT 
##   1.270614   3.483985   1.492601   1.664667   1.656170   2.223679 255.080687 
##  DPFEAOPFT  DPFEAOPFK  DPFEAINSP 
## 257.769209   2.662505   1.737183

4. does your model meet those assumptions? You don’t have to be perfectly right, just make a good case. ANSWER: Overall, I think my model meets most of the assumptions, like linearity and equal variance, but not all of them perfectly. The errors aren’t completely independent or normally distributed, and a few variables are highly correlated. Possibly suggesting that my model could be improved by removing or adjusting some predictors?

5. If your model violates an assumption, which one? ANSWER: My model violates the assumption of normality. The residuals aren’t normally distributed, which means the errors don’t follow the typical bell-shaped curve. This could slightly affect how accurate the model’s predictions and p-values are.

6. What would you do to mitigate this assumption? Show your work. ANSWER: I applied a log transformation to the dependent variable to make the residuals more normally distributed.

plot(district_model, which = 2)

district_model_log <- lm(log(DA0GR21N) ~ DPSTURNR + DPFRAALLK, data = clean_district)

plot(district_model_log, which = 2)

shapiro.test(residuals(district_model_log))

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(district_model_log)
## W = 0.99289, p-value = 0.1283