# Load necessary package and data
if (!require(wooldridge)) {
  install.packages("wooldridge")
}
## Loading required package: wooldridge
library(wooldridge)
data("discrim")

# Part (i): Calculate means and standard deviations
mean_prpblck <- mean(discrim$prpblck, na.rm = TRUE)
sd_prpblck <- sd(discrim$prpblck, na.rm = TRUE)
mean_income <- mean(discrim$income, na.rm = TRUE)
sd_income <- sd(discrim$income, na.rm = TRUE)
cat("Mean and SD of prpblck:", mean_prpblck, sd_prpblck, "\n")
## Mean and SD of prpblck: 0.1134864 0.1824165
cat("Mean and SD of income:", mean_income, sd_income, "\n")
## Mean and SD of income: 47053.78 13179.29
# Part (ii): OLS regression
model1 <- lm(psoda ~ prpblck + income, data = discrim)
summary(model1)
## 
## 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
# Part (iii): Simple regression without income
model2 <- lm(psoda ~ prpblck, data = discrim)
summary(model2)
## 
## 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
# Part (iv): Log-linear model
model3 <- lm(log(psoda) ~ prpblck + log(income), data = discrim)
summary(model3)
## 
## 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
# Part (v): Add prppov to the model
model4 <- lm(log(psoda) ~ prpblck + log(income) + prppov, data = discrim)
summary(model4)
## 
## 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
# Part (vi): Correlation between log(income) and prppov
correlation <- cor(log(discrim$income), discrim$prppov, use = "complete.obs")
cat("Correlation between log(income) and prppov:", correlation, "\n")
## Correlation between log(income) and prppov: -0.838467

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