For the data set

(a) Construct a correlation matrix between x1, x2, x3, and y. Is there any evidence that multicollinearity exists? Why?
(b) Determine the multiple regression line with x1, x2, and x3 as the explanatory variables.
(c) Assuming that the requirements of the model are satisfied, test H0: b1 = b2 = b3 = 0 versus H1: at least one of the bi is different from zero at the a = 0.05 level of significance.
(d) Assuming that the requirements of the model are satisfied, test H0: bi = 0 versus H1: bi ≠ 0 for i = 1, 2, 3 at the a = 0.05 level of significance. Should a variable be removed from the model? Why?
(e) Remove the variable identified in part (d) and recomputed the regression model. Test whether at least one regression coefficient is different from zero. Then test whether each individual regression coefficient is significantly different from zero.

24.9 13.5 3.7 59.8 66.3 26.7 15.7 11.4 30.6 13.8 15.7 76.5 39.6 8.8 8.8 77.1 33.1 10.6 18.3 81.9 41.1 9.7 21.8 84.6 16.4 25.4 9.8 87.3 33.8 6.8 25.9 88.5 23.5 7.5 15.5 90.7 39.8 6.8 30.8 93.4