library(wooldridge)
data("vote1")
#(i)
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
beta_2 <- coef(model)["expendA"]
beta_3 <- coef(model)["expendB"]
beta_4 <- coef(model)["I(expendA * expendB)"]
expendA_val <- 300 # Example value for expendA
expendB_val <- 100 # Example value for expendB
partial_effect_expendB <- beta_3 + beta_4 * expendA_val
cat("Partial effect of expendB on voteA:", partial_effect_expendB, "\n")
## Partial effect of expendB on voteA: -0.03371269
partial_effect_expendA <- beta_2 + beta_4 * expendB_val
cat("Partial effect of expendA on voteA:", partial_effect_expendA, "\n")
## Partial effect of expendA on voteA: 0.03761799
# (ii)
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
# (iii)
beta_3 <- coef(model)["expendB"]
beta_4 <- coef(model)["I(expendA * expendB)"]
expendA_val <- 300
effect_expendB <- beta_3 + beta_4 * expendA_val
effect_expendB
## expendB
## -0.03371269
# (iv)
expendB_val <- 100
effect_expendA_increase <- (coef(model)["expendA"] + beta_4 * expendB_val) * 100
effect_expendA_increase
## expendA
## 3.761799
# (v)
vote1$shareA <- vote1$expendA / (vote1$expendA + vote1$expendB)
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
# (vi)
expendA_val <- 300
expendB_val <- 0
shareA_val <- expendA_val / (expendA_val + expendB_val)
predicted_voteA <- predict(model_share, newdata = data.frame(prtystrA = mean(vote1$prtystrA), shareA = shareA_val))
predicted_voteA
## 1
## 72.56214