Test the null hypothesis that the coefficients of the three

Question

Use high school grades and SAT scores to predict high grade point averages. Run a logistic regression to predict HIGPA using the three high school grade summaries and the two SAT scores as explanatory variables. We want to produce an analysis that is similar to that done for these data.

(a) Test the null hypothesis that the coefficients of the three high school grade summaries are zero; that is, test H₀: β_HSM = β_HSS = β_HSE = 0.

(b) Test the null hypothesis that the coefficients of the two SAT scores are zero; that is, test H₀: β_SATM = β_SATV = 0.

(c) What do you conclude from the tests in (a) and (b)?