The director of graduate studies at a large college of business has the objective of predicting the grade point average (GPA) of students in an MBA program. The director begins by using the Graduate Management Admission Test (GMAT) score. A sample of 20 students who have completed two years in the program is selected and stored in GPIGMAT.
a. Construct a scatter plot and, assuming a linear relationship, use the least squares method to compute the regression coefficients b0 and b1.
b. Interpret the meaning of the Y intercept, b0, and the slope, b1, in this problem.
c. Use the prediction line developed in (a) to predict the mean GPA for a student with a GMAT score of 600.
d. Determine the coefficient of determination, r2, and interpret its meaning in this problem.
e. Perform a residual analysis on your results and evaluate the regression assumptions.
f. At the 0.05 level of significance, is there evidence of a linear relationship between GMAT score and GPA?
g. Construct a 95% confidence interval estimate of the mean GPA of students with a GMAT score of 600 and a 95% prediction interval of the GPA for a particular student with a GMAT score of 600.
h. Construct a 95% confidence interval estimate of the population slope.
i. What conclusions can you reach concerning the relationship between GMAT score and GPA?