In a multiple regression model using 400 students to explain college grade point average, the following explanatory variables and a constant term equal to 1 are initially included in the regression: high school GPA, ACT score, number of credits completed, mother's years of education, and father's years of education. The R^2 is .5. When the two parents' education variables are dropped, the R^2 becomes .4. Are the parents' education variables significant at the 1% significance level? Specifically, state the null and alternative hypotheses, relevant test statistic, critical value, and a short explanation for how you reached your conclusion. (Hint: remember that the lectures and the book both explain how to conduct an F-test of joint significance using R^2 values from two regressions)

Consider the following estimated regression that is the augmented version of the model to explain the standardized outcome on a final exam from question 1:

1.2964+.0062atndrte-1.4911priGPA-.118ACT+.3589priGPA^2 +.0043ACT^2

(1.2298)    (.0023)              (.4694)      (.0982)        (.0886)      (.0022)

n = 680;              R^2 = .2267            SSR = 514.0371

• According to this estimated regression, at about what prior college grade point average does the standardized outcome on the final exam reach its lowest level, other things equal?

b. Suppose there are two students who are otherwise identical, except that student A had an ACT score that was 10 points higher than that of student B. According to this estimated regression, what is the predicted difference in the standardized outcome on the final exam between student A and student B, other things equal?

c. Suppose that hwrte (percentage of homework turned in) is positively correlated with atndrte and has a direct positive effect on stndfnl. What would happen to the estimated coefficient of atndrte if hwrte were added into the above regression?