For the following data set:

a. Construct the multiple regression equation

b. Predict the value of y when x1 = 5.2, x2 = 9.1, x3 = 8.7, x4 = 2.8.

c. What percentage of the variation in y is explained by the model?

d. Is the model useful for prediction? Why or why not? Use the α = 0.01 level.

e. Test H0: β1 = 0 versus H1: β1 ≠ 0 at the α = 0.05 level. Can you reject H0? Repeat for β2 and β3.

y x1 x2 x3 X4 27.4 12.3 4.7 3.4 4.2 55.2 9.7 12.9 10.7 2.1 35.3 12.4 2.8 9.1 9.7 36.3 5.2 13.6 5.0 0.7 42.7 1.0 9.3 2.6 13.5 58.5 14.8 9.1 3.2 10.1 58.9 5.9 11.1 3.7 4.2 54.0 11.7 11.8 8.6 0.8 64.2 3.7 14.7 1.8 14.6 61.1 13.3 12.1 0.4 2.3 53.3 14.5 9.4 6.3 10.0 59.5 5.0 9.6 13.4 14.7 43.3 4.1 7.0 10.4 9.4 40.3 2.4 9.0 8.3 6.2 43.3 3.8 6.9 7.8 11.3