##Part1
# Load the wooldridge package and data
library(wooldridge)
data("vote1")
# Estimate the model with interaction term
model <- lm(voteA ~ prtystrA + expendA + expendB + I(expendA * expendB), data = vote1)
summary(model)
##
## Call:
## lm(formula = voteA ~ prtystrA + expendA + expendB + I(expendA *
## expendB), data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.9999 -8.7632 -0.1726 8.2310 29.7325
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.212e+01 4.591e+00 6.995 5.99e-11 ***
## prtystrA 3.419e-01 8.799e-02 3.886 0.000146 ***
## expendA 3.828e-02 4.960e-03 7.718 1.00e-12 ***
## expendB -3.172e-02 4.588e-03 -6.915 9.32e-11 ***
## I(expendA * expendB) -6.629e-06 7.186e-06 -0.923 0.357584
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.13 on 168 degrees of freedom
## Multiple R-squared: 0.5708, Adjusted R-squared: 0.5606
## F-statistic: 55.86 on 4 and 168 DF, p-value: < 2.2e-16
##Part2
#As it shows an error in the values, it cannot be statistically significant
##Part3
# Calculate the mean of expendA
mean_expendA <- mean(vote1$expendA, na.rm = TRUE)
# Set expendA to 300 and increase expendB by 100
expendA_value <- 300
delta_expendB <- 100
# Calculate the partial effect using the estimated coefficients
coefficients <- coef(model)
effect_increase_expendB <- coefficients["expendB"] + coefficients["I(expendA * expendB)"] * expendA_value
# Print the effect
effect_increase_expendB * delta_expendB
## expendB
## -3.371269
##Part4
# Set expendB to 100 and calculate effect of increasing expendA by 100
expendB_value <- 100
delta_expendA <- 100
# Calculate the partial effect of expendA
effect_increase_expendA <- coefficients["expendA"] + coefficients["I(expendA * expendB)"] * expendB_value
# Print the effect
effect_increase_expendA * delta_expendA
## expendA
## 3.761799
# Calculate shareA
vote1$shareA <- vote1$expendA / (vote1$expendA + vote1$expendB)
# Estimate the new model without the interaction term
model_share <- lm(voteA ~ prtystrA + shareA, data = vote1)
summary(model_share)
##
## Call:
## lm(formula = voteA ~ prtystrA + shareA, data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.7258 -3.7460 -0.0886 3.0517 30.7756
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.85013 2.41558 8.218 5.08e-14 ***
## prtystrA 0.15320 0.04962 3.087 0.00236 **
## shareA 45.08931 1.47955 30.475 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.231 on 170 degrees of freedom
## Multiple R-squared: 0.8638, Adjusted R-squared: 0.8622
## F-statistic: 539 on 2 and 170 DF, p-value: < 2.2e-16
# Set expendA = 300 and expendB = 0
expendA_fixed <- 300
expendB_fixed <- 0
# Calculate shareA with expendB = 0
shareA_fixed <- expendA_fixed / (expendA_fixed + expendB_fixed)
# Calculate partial effect of expendB on voteA numerically
model_share_effect <- lm(voteA ~ prtystrA + I(expendA / (expendA + expendB)), data = vote1)
summary(model_share_effect)
##
## Call:
## lm(formula = voteA ~ prtystrA + I(expendA/(expendA + expendB)),
## data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.7258 -3.7460 -0.0886 3.0517 30.7756
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.85013 2.41558 8.218 5.08e-14 ***
## prtystrA 0.15320 0.04962 3.087 0.00236 **
## I(expendA/(expendA + expendB)) 45.08931 1.47955 30.475 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.231 on 170 degrees of freedom
## Multiple R-squared: 0.8638, Adjusted R-squared: 0.8622
## F-statistic: 539 on 2 and 170 DF, p-value: < 2.2e-16
# Evaluate the effect at expendA = 300 and expendB = 0
share_effect <- coefficients(model_share_effect)["I(expendA / (expendA + expendB))"]
share_effect
## <NA>
## NA