PAD 6833 HW #7

1. Load your preferred dataset into R studio

library(tidyverse)

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library(readxl)
library(ggplot2)
library(MASS)

## 
## Attaching package: 'MASS'
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## The following object is masked from 'package:dplyr':
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##     select

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(car)

## Loading required package: carData
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## Attaching package: 'car'
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## The following object is masked from 'package:dplyr':
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##     recode
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## The following object is masked from 'package:purrr':
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CountyClean<-read_excel("CountyClean.xlsx")

## New names:
## • `National Z-Score` -> `National Z-Score...11`
## • `National Z-Score` -> `National Z-Score...24`

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

Dependent Variable: # Drug Overdose Deaths (DOD) Independent Variables: Primary Care Physician Rate (PCP), Mental Health Provider Rate (MHP), Unemployment Rate (UNEM), # of Uninsured Adults (UNIN), and Severe Housing Cost Burden Rate (HSHCB)

county_model1<-lm(DOD~UNIN+HSHCB+PCP+MHP+UNEM,data=CountyClean)

3. Check the following assumptions:

1. Linearity (plot and raintest)

plot(county_model1,which=1)

This model is not linear based on visual inspection.

2. Independence of errors (durbin-watson)

durbinWatsonTest(county_model1)

##  lag Autocorrelation D-W Statistic p-value
##    1     -0.03458428      2.069099    0.73
##  Alternative hypothesis: rho != 0

The model’s errors are independent per Durbinwatson test as the p-value is 0.706 and over 0.05.

3. Homoscedasticity (plot, bptest)

plot(county_model1,which=3)

bptest(county_model1)

## 
##  studentized Breusch-Pagan test
## 
## data:  county_model1
## BP = 2.6562, df = 5, p-value = 0.7528

Model is homoskedastic per bp-test (p value > 0.05)

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

plot(county_model1,which=2)

Model is mostly abnormal by visual inspection as the data points stray from the line.

5. No multicolinarity (VIF, cor)

vif(county_model1)

##      UNIN     HSHCB       PCP       MHP      UNEM 
## 1299.4470 3177.9897  917.2266  632.7910 2038.8465

This model has multicolinearity.

4. does your model meet those assumptions? You don’t have to be perfectly right, just make a good case.

The model meets the assumptions of the Independence of Errors and Homoskedasticity

5. If your model violates an assumption, which one?

My model violates the assumptions of linearity, Normality of Residuals and multicoliniarity

6. What would you do to mitigate this assumption? Show your work.

LINEAR TRANSFORMATION:

county_model_log1<-lm(DOD~UNIN+HSHCB+PCP+MHP+UNEM,data=CountyClean)

plot(county_model_log1,which=1)

Model was log transformed to help with linearity but the final result was still nonlinear

NORMALITY OF RESIDUALS:

shapiro.test(county_model1$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  county_model1$residuals
## W = 0.77955, p-value = 1.705e-11

county_model2<-lm(log(DOD)~UNIN+HSHCB+PCP+MHP+UNEM,data=CountyClean)

shapiro.test(county_model2$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  county_model2$residuals
## W = 0.92039, p-value = 6.578e-06

plot(county_model2,which=2)

This somewhat fixed the violation but the model is still somewhat abnormal.

MULTICOLINEARITY:

kitchen_sink<-lm(DOD~UNIN+HSHCB+PCP+MHP+UNEM,data=CountyClean)

vif(kitchen_sink)

##      UNIN     HSHCB       PCP       MHP      UNEM 
## 1299.4470 3177.9897  917.2266  632.7910 2038.8465

Model was transformed to help with Multicolinearity but the variables still violate no multivolinearity