Nathan’s Homework 7

library(tidyverse)

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library(ggplot2)
library(readxl)
library(pastecs)

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library(lmtest)

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library(MASS)

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library(car)

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HousingData <- read_csv("Table9.csv")

## Rows: 3221 Columns: 152
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## chr   (6): source, sumlevel, geoid, name, st, cnty
## dbl (146): T9_est1, T9_est2, T9_est3, T9_est4, T9_est5, T9_est6, T9_est7, T9...
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CHAS_renters <- HousingData %>%
  mutate(
    severe_prob_rate = (T9_est5 / T9_est1) * 100,
    overcrowd_rate = (T9_est10 / T9_est1) * 100,
    incomplete_rate = ((T9_est12 + T9_est13) / T9_est1) * 100
  )

model <- lm(severe_prob_rate ~ overcrowd_rate + incomplete_rate, data = CHAS_renters)

summary(model)

## 
## Call:
## lm(formula = severe_prob_rate ~ overcrowd_rate + incomplete_rate, 
##     data = CHAS_renters)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.0394 -1.2284 -0.0352  1.3681 10.8438 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.03935    0.04795 125.947   <2e-16 ***
## overcrowd_rate  -0.63794    0.03476 -18.352   <2e-16 ***
## incomplete_rate -0.05017    0.02477  -2.025   0.0429 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.302 on 3218 degrees of freedom
## Multiple R-squared:  0.09888,    Adjusted R-squared:  0.09832 
## F-statistic: 176.6 on 2 and 3218 DF,  p-value: < 2.2e-16

plot(model, which = 1)

raintest(model) 

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##  Rainbow test
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## data:  model
## Rain = 1.5521, df1 = 1611, df2 = 1607, p-value < 2.2e-16

dwtest(model) 

## 
##  Durbin-Watson test
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## data:  model
## DW = 1.3254, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0

plot(model, which = 3)

bptest(model)

## 
##  studentized Breusch-Pagan test
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## data:  model
## BP = 52.188, df = 2, p-value = 4.65e-12

plot(model, which = 2)  

res <- resid(model)       
shapiro.test(res)

## 
##  Shapiro-Wilk normality test
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## data:  res
## W = 0.9805, p-value < 2.2e-16

vif(model)

##  overcrowd_rate incomplete_rate 
##        1.011949        1.011949

#The model does not meet all of the assumptions. It violates linearity of variables and independence of errors. There is some issues with mormality of the residuals but this is a large dataset so that could influence the results.

#I would use a log transformed model to improve the fit.