library(wooldridge)
data <- wooldridge::discrim
# (i)
model1 <- lm(log(psoda) ~ prpblck + log(income) + prppov, data = data)
summary(model1)
##
## Call:
## lm(formula = log(psoda) ~ prpblck + log(income) + prppov, data = data)
##
## 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
#(ii)
correlation <- cor(log(data$income), data$prppov)
cat("Correlation between log(income) and prppov: ", correlation, "\n")
## Correlation between log(income) and prppov: NA
cor_test <- cor.test(log(data$income), data$prppov)
print(cor_test)
##
## Pearson's product-moment correlation
##
## data: log(data$income) and data$prppov
## t = -31.04, df = 407, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.8650980 -0.8071224
## sample estimates:
## cor
## -0.838467
#(iii)
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
#(iv)
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
#(v)
cat("R-squared of model 1: ", summary(model1)$r.squared, "\n")
## R-squared of model 1: 0.08696154
cat("R-squared of model 2: ", summary(model2)$r.squared, "\n")
## R-squared of model 2: 0.1839299
cat("AIC of model 1: ", AIC(model1), "\n")
## AIC of model 1: -868.0719
cat("AIC of model 2: ", AIC(model2), "\n")
## AIC of model 2: -911.0953
cat("BIC of model 1: ", BIC(model1), "\n")
## BIC of model 1: -848.1021
cat("BIC of model 2: ", BIC(model2), "\n")
## BIC of model 2: -887.1315