For the following 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 final model constructed in part (c) to predict the value of y if x1 = 44.3, x2 = 1.1, x3 = 7, and x4 = 69.
(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 = 44.3, x2 = 1.1, x3 = 7, and x4 = 69.

x2 X4 47.3 0.9 4 76 105.5 113.8 53.1 0.8 6. 55 56.7 0.8 65 115.2 48.8 0.5 67 118.9 42.7 1.1 74 148.9 6. 44.3 1.1 76 120.2 44.5 0.7 68 121.6 0.7 37.7 79 140.0 36.9 1.0 73 141.5 28.1 1.8 6. 68 141.9 32.0 0.8 81 152.8 34.7 0.8 10 68 156.5