The U.S. Bureau of Labor Statistics produces consumer price indexes for several different categories. Shown here are the percentage changes in consumer price indexes over a period of 20 years for food, shelter, apparel, and fuel oil. Also displayed are the percentage changes in consumer price indexes for all commodities. Use these data and multiple regression to develop a model that attempts to predict all commodities by the other four variables.

All Fuel
Commodities / Food /Shelter /Apparel /Oil
0.9 1.0 2.0 1.6 3.7
0.6 1.3 0.8 0.9 2.7
0.9 0.7 1.6 0.4 2.6
0.9 1.6 1.2 1.3 2.6
1.2 1.3 1.5 0.9 2.1
1.1 2.2 1.9 1.1 2.4
2.6 5.0 3.0 2.5 4.4
1.9 0.9 3.6 4.1 7.2
3.5 3.5 4.5 5.3 6.0

The regression equation is (round all numbers to two decimal places):

All Commodities=+()*Food+()*Shelter+()*Apparel+()*Fuel Oil

The tolerance is +/- 0.05.