A statistics instructor wishes to investigate the relation between a student's final course grade and grades on a midterm exam and a major project. She selects a random sample of 10 statistics students and obtains the following information:

(a) Construct a correlation matrix between course grade, midterm grade, and project grade. Is there any reason to be concerned with multicollinearity based on the correlation matrix?
(b) Find the least-squares regression equation y̅ = b0 + b1x1 + b2x2, where x1 is the midterm exam score, x2 is the project score, and y is the final course grade.
(c) Draw residual plots, a boxplot of residuals, and a normal probability plot of the residuals to assess the adequacy of the model.
(d) Interpret the regression coefficients for the least-squares regression equation.
(e) Determine and interpret R2 and the adjusted R2.
(f) Test H0: b1 = b2 = 0 versus H1: at least one bi ≠ 0 at the a = 0.05 level of significance.
(g) Test the hypotheses H0: β1 = 0 versus H1: β1 ≠ 0 and H0: β2 = 0 versus H1: β2 ≠ 0 at the a = 0.05 level of significance. Should any of the explanatory variables be removed from the model?
(h) Predict the mean final course grade of all statistics students who have an 85 on their midterm and a 75 on their project.
(i) Construct and interpret 95% confidence and prediction intervals for statistics students who score an 83 on their midterm and a 92 on their project. Interpret the results.