Exercise 3 (Total: 20 Points) A researcher is studying factors that are associated with whether a person is married. The researcher uses data on a random sample of individuals: Description Variable marr age Indicator = 1 if person is married, 0 otherwise Age in years educ male south totwrk_hr Number of years of education Indicator = 1 if person is a male, 0 otherwise Indicator = 1 if person lives in the south, 0 otherwise Total hours the individual works in a week The researcher specifies two regressions: a linear probability model and a logistic regression/logit. Model 1: Im(marrage + educ + male + south + totwrk_hr, data = data) with heteroskedasticity- robust standard errors Model 2: glm(marr ~ age + educ + male + south + totwrk_hr, family = binomial(link="logit"), data = data) a) [4pts] Below is the regression output for model 1, the linear probability model. Interpret the coefficient on totwrk_hr and whether it significantly affects the probability of being married. Why did the researcher use heteroskedasticity-robust standard errors? OLS estimation, Dep. Var.: marr Observations: 706 Standard-errors: Heteroskedasticity-robust Estimate Std. Error t value Pr(>It!) (Intercept) 0.898254 0.099034 9.070133 -0.000167 < 2.2e-16 *** 0.001318 -0.126695 8.9922e-01 age educ male south -0.005436 0.005509 -0.986798 3.2408e-01 0.158772 0.033512 4.737733 2.6179e-06 *** -0.025907 0.039179 -0.661239 5.0868e-01 totwrk_hr -0.002429 --- 0.000933 -2.603174 9.4321e-03 ** Signif. codes: 0*** 0.001 **** 0.01 * 0.05 0.11 RMSE: 0.375364 Adj. R2: 0.03215 b) [5pts] In the logistic regression, the researcher estimates a coefficient on educ of -0.0403 with a p- value of 0.2894. The average marginal effect for the same coefficient is -0.0057 with a p-value of 0.2888. Which coefficient should the researcher use in their interpretation of the results? Interpret the coefficient that you select. c) [2pts] In the logistic regression, the researcher would like to test whether an individual's age, education, and whether they live in the south jointly affect the probability of being married. What additional regression should they run? State the dependent and independent variables. d) [6pts] After running the additional regression, the researcher gets a log-likelihood of -317.3224 for the unrestricted model and a log-likelihood of -318.1155 for the restricted model. Using this information, test whether an individual's age, education, and whether they live in the south jointly affect the probability of being married at the 90% significance level. e) [3pts] The researcher calculates predicted probabilities from both the linear probability model and the logistic regression and plots them against total hours worked per week. The researcher plots one model in red triangles and one model in blue circles. However, the researcher forgets to label the graph. Which model is the red triangles, and which is the blue circles? How do you know? Predicted probability 0.7- 0.6- 1.0- 0.9- 0 30 60 90 Total hours worked per week