Use the data in HTV to answer this question. See also Computer Exercise C10 in Chapter 3.

(i) Estimate the regression model educ 5 b0 1 b1motheduc 1 b2fatheduc 1 b3abil 1 b4abil2 1 u by OLS and report the results in the usual form. Test the null hypothesis that educ is linearly related to abil against the alternative that the relationship is quadratic.

(ii) Using the equation in part (i), test H0: b1 5 b2 against a two-sided alternative. What is the p-value of the test?

(iii) Add the two college tuition variables to the regression from part (i) and determine whether they are jointly statistically significant.

(iv) What is the correlation between tuit17 and tuit18? Explain why using the average of the tuition over the two years might be preferred to adding each separately. What happens when you do use the average?

(v) Do the findings for the average tuition variable in part (iv) make sense when interpreted causally? What might be going on?