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.

X4 43 19.6 7.1 32 200 44 13.1 58.5 37 204 40 24.7 2.1 32 215 35 30.4 41.4 39 229 38 28.2 7.7 30 231 39 24.9 25.0 26 243 39 45.7 28.5 25 266 38.4 40 27.7 24 278 47 36.9 26.2 17 287 35 66.3 4.2 23 298 36 112.8 26.2 21 339 44 108.4 22.3 24 359