Homework 7
Aaron Rodriguez
2025-04-03
library(ggplot2)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ lubridate 1.9.4 ✔ tibble 3.2.1
## ✔ purrr 1.0.2 ✔ tidyr 1.3.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(readxl)
library(ggplot2)
districtbasehw7 <- read_xls("district.xls")districtbasehw7cleaned<-districtbasehw7 %>% select(DISTNAME,DZCAMPUS,DAGC4X21R,DA0AT21R,DPSTURNR,DPSTKIDR,DPFEAINSP,DZEXADMP) %>% na.omit(.)Load your preferred dataset into R studio
Create a linear model “lm()” from the variables, with a continuous dependent variable as the outcome
hw7model2 <- lm(DAGC4X21R ~ DA0AT21R + DPSTURNR +
DPSTKIDR + DPFEAINSP + DZEXADMP, data = districtbasehw7cleaned)
summary(hw7model2)##
## Call:
## lm(formula = DAGC4X21R ~ DA0AT21R + DPSTURNR + DPSTKIDR + DPFEAINSP +
## DZEXADMP, data = districtbasehw7cleaned)
##
## Residuals:
## Min 1Q Median 3Q Max
## -95.800 -1.604 1.615 4.456 22.070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.375e+01 1.341e+01 -2.517 0.012 *
## DA0AT21R 1.683e+00 1.268e-01 13.279 < 2e-16 ***
## DPSTURNR 1.283e-03 4.140e-02 0.031 0.975
## DPSTKIDR 1.414e-04 1.409e-01 0.001 0.999
## DPFEAINSP -4.314e-01 8.586e-02 -5.024 5.92e-07 ***
## DZEXADMP -9.074e-01 1.386e-01 -6.547 9.10e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.6 on 1065 degrees of freedom
## Multiple R-squared: 0.1827, Adjusted R-squared: 0.1788
## F-statistic: 47.61 on 5 and 1065 DF, p-value: < 2.2e-16- Check the following assumptions:
- Linearity (plot and raintest)
plot(hw7model2,which = 1)
raintest
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(zoo)
raintest(hw7model2)##
## Rainbow test
##
## data: hw7model2
## Rain = 0.97204, df1 = 536, df2 = 529, p-value = 0.6283- Independence of errors (durbin-watson)
dw_hw7model<-dwtest(hw7model2)
print(dw_hw7model)##
## Durbin-Watson test
##
## data: hw7model2
## DW = 1.7985, p-value = 0.0004514
## alternative hypothesis: true autocorrelation is greater than 0- Homoscedasticity (plot, bptest)
plot(hw7model2,which= 3)
Bptest
library(lmtest)
bp_resulthw7<-bptest(hw7model2)
print(bp_resulthw7)##
## studentized Breusch-Pagan test
##
## data: hw7model2
## BP = 55.017, df = 5, p-value = 1.295e-10- Normality of residuals (QQ plot, shapiro test) lk,
plot(hw7model2, which = 2)
Shapiro test
shw7model2<-residuals(hw7model2)
shap_testhw7<- shapiro.test(shw7model2)
print(shap_testhw7)##
## Shapiro-Wilk normality test
##
## data: shw7model2
## W = 0.50561, p-value < 2.2e-16- No multicolinarity (VIF, cor)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
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## recode## The following object is masked from 'package:purrr':
##
## somevifhw7<-vif(hw7model2)
print(vifhw7)## DA0AT21R DPSTURNR DPSTKIDR DPFEAINSP DZEXADMP
## 1.091423 1.139951 1.222410 1.389638 1.602137cor
predictors <- districtbasehw7cleaned[, c("DA0AT21R", "DPSTURNR",
"DPSTKIDR", "DPFEAINSP", "DZEXADMP")]
print(predictors)## # A tibble: 1,071 × 5
## DA0AT21R DPSTURNR DPSTKIDR DPFEAINSP DZEXADMP
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 96.7 19.1 12.3 49.6 9.1
## 2 96 13.9 11 60.3 6.9
## 3 95.4 21.6 10.8 54.2 8.3
## 4 95.8 18.3 11.3 53.7 10.7
## 5 93.7 17.9 12.9 54.6 8.3
## 6 94.5 30.6 11 50.6 8.5
## 7 96.7 14.6 9.3 61.7 6.4
## 8 92.8 11.5 14.4 56.7 7.6
## 9 97.3 17 14.8 58.7 12.8
## 10 95.2 9.5 13.2 58.5 4.6
## # ℹ 1,061 more rows- does your model meet those assumptions? You don’t have to be perfectly right, just make a good case.
I think of the test the one that isnt violated is the rainbow test. The p value is greater than 0.05.
- If your model violates an assumption, which one?
The easiest one to see is through the visual representation of the homoscedasticity. The red line clearly curves and the actual plots of data pop up very far from the line. THis shows my data is heteroscedasticity.
- What would you do to mitigate this assumption? Show your work.
I would work on the Heteroscedasticity by squaring my data. I think it helps the curve of the redline but there is more work to be done. The data is much too clumped together still.
hw7model2_sq <- lm(DAGC4X21R ~ I(DA0AT21R^2) + I(DPSTURNR^2) + I(DPSTKIDR^2) +
I(DPFEAINSP^2) + I(DZEXADMP^2), data = districtbasehw7cleaned)
plot(hw7model2_sq)
