For the following data set: 

a. Construct the multiple regression equation ̂y = b0 + b1x1 + b2x2 + b3x3.

b. Predict the value of y when x1 = 1, x2 = 4.5, x3 = 6.2.

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 and β3.

y x1 *2 x3 13.9 4.1 0.6 0.1 47.2 8.4 4.4 9.3 21.9 6.9 2.8 1.1 27.9 6.0 0.0 7.2 48.1 6.2 2.9 9.1 44.1 0.9 8.0 7.7 49.7 6.9 7.6 9.0 32.7 7.3 2.2 4.7 30.6 9.7 4.3 3.7 41.1 6.9 1.5 7.4