library(discrim)
## Loading required package: parsnip
library(wooldridge)
library(tidyverse)
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## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2
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## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
model1 <- lm(log(psoda) ~ prpblck + log(income) + prppov, data = discrim)
summary(model1)
## 
## Call:
## lm(formula = log(psoda) ~ prpblck + log(income) + prppov, data = discrim)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32218 -0.04648  0.00651  0.04272  0.35622 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.46333    0.29371  -4.982  9.4e-07 ***
## prpblck      0.07281    0.03068   2.373   0.0181 *  
## log(income)  0.13696    0.02676   5.119  4.8e-07 ***
## prppov       0.38036    0.13279   2.864   0.0044 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08137 on 397 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.08696,    Adjusted R-squared:  0.08006 
## F-statistic:  12.6 on 3 and 397 DF,  p-value: 6.917e-08
model_income <- lm(log(income) ~ prppov, data = discrim)
summary(model_income)
## 
## Call:
## lm(formula = log(income) ~ prppov, data = discrim)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37088 -0.10394 -0.01445  0.09566  0.90712 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 10.97211    0.01118  981.74   <2e-16 ***
## prppov      -3.53694    0.11395  -31.04   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1552 on 407 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.703,  Adjusted R-squared:  0.7023 
## F-statistic: 963.5 on 1 and 407 DF,  p-value: < 2.2e-16
model_prppov <- lm(prppov ~ log(income), data = discrim)
summary(model_prppov)
## 
## Call:
## lm(formula = prppov ~ log(income), data = discrim)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.083653 -0.023897 -0.006352  0.021363  0.163744 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.202066   0.068670   32.07   <2e-16 ***
## log(income) -0.198767   0.006404  -31.04   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0368 on 407 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.703,  Adjusted R-squared:  0.7023 
## F-statistic: 963.5 on 1 and 407 DF,  p-value: < 2.2e-16
model2 <- lm(log(psoda) ~ prpblck + log(income) + prppov + log(hseval), data = discrim)
summary(model2)
## 
## Call:
## lm(formula = log(psoda) ~ prpblck + log(income) + prppov + log(hseval), 
##     data = discrim)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.30652 -0.04380  0.00701  0.04332  0.35272 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.84151    0.29243  -2.878 0.004224 ** 
## prpblck      0.09755    0.02926   3.334 0.000937 ***
## log(income) -0.05299    0.03753  -1.412 0.158706    
## prppov       0.05212    0.13450   0.388 0.698571    
## log(hseval)  0.12131    0.01768   6.860 2.67e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07702 on 396 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.1839, Adjusted R-squared:  0.1757 
## F-statistic: 22.31 on 4 and 396 DF,  p-value: < 2.2e-16
model2 <- lm(log(psoda) ~ prpblck + log(income) + prppov + log(hseval), data = discrim)
summary(model2)
## 
## Call:
## lm(formula = log(psoda) ~ prpblck + log(income) + prppov + log(hseval), 
##     data = discrim)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.30652 -0.04380  0.00701  0.04332  0.35272 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.84151    0.29243  -2.878 0.004224 ** 
## prpblck      0.09755    0.02926   3.334 0.000937 ***
## log(income) -0.05299    0.03753  -1.412 0.158706    
## prppov       0.05212    0.13450   0.388 0.698571    
## log(hseval)  0.12131    0.01768   6.860 2.67e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07702 on 396 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.1839, Adjusted R-squared:  0.1757 
## F-statistic: 22.31 on 4 and 396 DF,  p-value: < 2.2e-16
anova(model1, model2)
## Analysis of Variance Table
## 
## Model 1: log(psoda) ~ prpblck + log(income) + prppov
## Model 2: log(psoda) ~ prpblck + log(income) + prppov + log(hseval)
##   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
## 1    397 2.6284                                  
## 2    396 2.3493  1   0.27915 47.054 2.668e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

```