Use the data in CATHOLIC to answer this question.

(i) In the entire sample, what percentage of the students attend a Catholic high school? What is the average of math12 in the entire sample?

(ii) Run a simple regression of math12 on cathhs and report the results in the usual way. Interpret what you have found.

(iii) Now add the variables lfaminc, motheduc, and fatheduc to the regression from part (ii). How many observations are used in the regression? What happens to the coefficient on cathhs, along with its statistical significance?

(iv) Return to the simple regression of math12 on cathhs, but restrict the regression to observations used in the multiple regression from part (iii). Do any important conclusions change?

(v) To the multiple regression in part (iii), add interactions between cathhs and each of the other explanatory variables. Are the interaction terms individually or jointly significant?

(vi) What happens to the coefficient on cathhs in the regression from part (v). Explain why this coefficient is not very interesting.

(vii) Compute the average partial effect of cathhs in the model estimated in part (v). How does it compare with the coefficients on cathhs in parts (iii) and (v)?