The computer output below shows a multiple regression model to predict grade point average (GPA) using six variables from the dataset SleepStudy. Gender is coded 0 for females and 1 for males; ClassYear is coded 1 for first year, 2 for sophomore, 3 for junior, and 4 for senior; ClassesMissed is number of classes missed during the semester; CognitionZscore is a normalized z-score of results from cognitive skills tests; DASScore is a combined measure of depression, anxiety, and stress with higher numbers indicating more depression, anxiety, or stress; Drinks is the number of alcoholic drinks consumed in a week.

The regression equation is GPA = 3.49 ˆ’ 0.0971 Gender ˆ’ 0.0558 ClassYear ˆ’ 0.0146 ClassesMissed + 0.118 CognitionZscore + 0.00284 DASScore ˆ’ 0.0163 Drinks

(a) Interpret the coefficients of Gender, ClassYear, and ClassesMissed in context. Be sure to pay attention to how the first two variables are coded.
(b) Use the p-value from the ANOVA test to determine whether the model is effective.
(c) Interpret R² in context.
(d) Which explanatory variable is most significant in the model? Which is least significant?
(e) Which variables are significant at a 5% level?

Predictor Coef SE Coef Constant 3.48759 0.07497 46.52 0.000 -1.82 0.069 Gender -0.09714 0.05326 ClassYear -0.05583 0.02284 -2.44 0.015 ClassesMissed CognitionZscore -0.014613 0.007467 0.11837 -1.96 0.051 0.03421 3.46 0.001 DASScore 0.002844 0.001441 1.97 0.049 Drinks -0.016336 0.006241 -2.62 0.009 R-Sq = 18.4% R-Sq(adj) = 16.4% Analysis of Variance Source DF MS Regression 7.5925 1.2654 9.27 0.000 Residual Error 246 33.5958 0.1366 Total 252 41.1884