library(wooldridge)
library(car)
## Loading required package: carData
data("discrim")
# Calculate mean and standard deviation for prpblck and income
mean_prpblck <- mean(discrim$prpblck, na.rm = TRUE)
mean_income <- mean(discrim$income, na.rm = TRUE)
sd_prpblck <- sd(discrim$prpblck, na.rm = TRUE)
sd_income <- sd(discrim$income, na.rm = TRUE)
mean_prpblck
## [1] 0.1134864
mean_income
## [1] 47053.78
sd_prpblck
## [1] 0.1824165
sd_income
## [1] 13179.29
#2 OLS regression for psoda on prpblck and income
model_ols <- lm(psoda ~ prpblck + income, data = discrim)
summary(model_ols)
##
## Call:
## lm(formula = psoda ~ prpblck + income, data = discrim)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.29401 -0.05242 0.00333 0.04231 0.44322
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.563e-01 1.899e-02 50.354 < 2e-16 ***
## prpblck 1.150e-01 2.600e-02 4.423 1.26e-05 ***
## income 1.603e-06 3.618e-07 4.430 1.22e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08611 on 398 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.06422, Adjusted R-squared: 0.05952
## F-statistic: 13.66 on 2 and 398 DF, p-value: 1.835e-06
#3 Simple regression of psoda on prpblck
model_simple <- lm(psoda ~ prpblck, data = discrim)
summary(model_simple)
##
## Call:
## lm(formula = psoda ~ prpblck, data = discrim)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.30884 -0.05963 0.01135 0.03206 0.44840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.03740 0.00519 199.87 < 2e-16 ***
## prpblck 0.06493 0.02396 2.71 0.00702 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0881 on 399 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.01808, Adjusted R-squared: 0.01561
## F-statistic: 7.345 on 1 and 399 DF, p-value: 0.007015
#4 Log-log regression model
model_log <- lm(log(psoda) ~ prpblck + log(income), data = discrim)
summary(model_log)
##
## Call:
## lm(formula = log(psoda) ~ prpblck + log(income), data = discrim)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.33563 -0.04695 0.00658 0.04334 0.35413
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.79377 0.17943 -4.424 1.25e-05 ***
## prpblck 0.12158 0.02575 4.722 3.24e-06 ***
## log(income) 0.07651 0.01660 4.610 5.43e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0821 on 398 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.06809, Adjusted R-squared: 0.06341
## F-statistic: 14.54 on 2 and 398 DF, p-value: 8.039e-07
coef_prpblck <- coef(model_log)["prpblck"]
# Percentage change in psoda for a 0.20 increase in prpblck
percentage_change <- 0.20 * coef_prpblck
percentage_change
## prpblck
## 0.02431605
#5 Log-log regression with prppov included
model_prppov <- lm(log(psoda) ~ prpblck + log(income) + prppov, data = discrim)
summary(model_prppov)
##
## 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
#6 Correlation between log(income) and prppov
correlation <- cor(log(discrim$income), discrim$prppov, use = "complete.obs")
correlation
## [1] -0.838467
#7 Calculate VIF for the model with prppov
vif(model_prppov)
## prpblck log(income) prppov
## 1.922160 3.518721 4.915220