For the following data set:

a. Construct the multiple regression equation

b. Predict the value of y when x1 = 15.3, x2 = 4.7, x3 = 0.6, x4 = 8.2.

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 = 0.05 level.

e. Test H0: β1 = 0 versus H1: β1 ≠ 0 at the α = 0.05 level. Can you reject H0? Repeat for β2. β3 and β4.

y x1 x2 x3 x4 163.4 2.9 24.2 4.3 4.4 120.9 22.2 12.9 10.6 13.7 116.7 5.5 6.8 17.3 13.9 63.9 8.8 12.0 0.9 1.2 86.9 5.1 18.3 2.5 13.4 74.2 14.7 8.0 8.5 5.6 72.8 7.1 17.2 0.2 24.7 84.1 1.6 5.6 0.5 4.3 136.4 21.6 2.0 3.9 15.7 122.3 14.5 13.3 14.7 13.1 78.9 17.7 12.7 3.2 8.0 108.0 16.4 15.0 1.6 23.3 124.5 24.3 20.6 9.1 11.3 90.9 21.7 0.6 5.7 5.8 143.5 18.6 11.2 13.9 14.7