For the data set

(a) Construct a correlation matrix between x1, x2, x3, x4, and y. Is there any evidence that multicollinearity may be a problem?
(b) Determine the multiple regression line using all the explanatory variables listed. Does the F-test indicate that we should reject H0: b1 = b2 = b3 = b4 = 0? Which explanatory variables have slope coefficients that are not significantly different from zero?
(c) Remove the explanatory variable with the highest P-value from the model and recompute the regression model. Does the F-test still indicate that the model is significant? Remove any additional explanatory variables on the basis of the P-value of the slope coefficient. Then compute the model with the variable removed.
(d) Draw residual plots and a boxplot of the residuals to assess the adequacy of the model.
(e) Use the model constructed in part (c) to predict the value of y if x1 = 34, x2 = 35.6, x3 = 12.4, and x4 = 29.
(f) Draw a normal probability plot of the residuals. Is it reasonable to construct confidence and prediction intervals?
(g) Construct 95% confidence and prediction intervals if x1 = 34, x2 = 35.6, x3 = 12.4, and x4 = 29.