1. The data set provided to you gives information on employee wages and years of education beyond high school. Do the following (do not use excel features or STATA features for estimation):

a. Estimate the regression equation of wage on educ. Write down formally the regression equation with standard errors underneath within parenthesis.
b. Find R² for this problem and interpret R².

2. The following model was fitted to data from 50 US states.

y = Annual salary of chief justice of the state supreme court
x₁ = Average annual salary of lawyers, in thousands of dollars,
x₂ = number of bills enacted in previous legislative session,
x₃ = number of due process reviews by state courts that resulted in overturn of legislation in previous 40 years,
x₄ = length of term of the chief justice of the state supreme court,
x₅ = dummy variable, taking the value 1 if Supreme Court justices are elected on partisan ballot, and 0 otherwise.

R²= 0.54

a. Interpret the coefficient associated with x₂.

b. Interpret the coefficient associated with x₅.

c. Write down in your BLUE book the values of (1) through (9) using the following ANOVA Table.

ANOVA TABLE

d. Using the p-value approach, test at 5 percent level if all the variables as a group has any influence on the annual salary of Chief Justice. Write all the steps for the test as we do in class.