# In a multiple regression model using 400 students

March 14, 2016

Question

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

a). Test, at the 5% significance level, the hypothesis that students with higher attendance rate tend to have higher standardized outcome on the final exam. Specifically, state the null and alternative hypotheses, relevant test statistic, critical value, and a short explanation for how you reached your conclusion.

b). Suppose you are also given the following estimated regression:

stnddfnl = -3:3437 +.0053atndrte +.4024priGPA +.0843ACT

(0.2991) (.0024) (.0783) (.0111)

n = 680; SSR = 530.941

Test, at the 1% significance level, the hypothesis that priGPA2 and ACT2 jointly have no effect on stndfnl. Specifically, state the null and alternative hypotheses, relevant test statistic, critical value, and a short explanation for how you reached your conclusion.

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