The U.S. Bureau of Labor Statistics produces consumer price indexes for several

Question

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. Comment on the result of this analysis.

The regression equation is (Round all numbers to 4 decimal places):

All Commodities=

+ (

) Food+(

) Shelter + (

) Apparel + (

) Fuel Oil

All Fuel Commodities Food Shelter Apparel Oil .9 1.0 2.0 1.6 3.7 .6 1.3 .8 .9 2.7 .9 .7 1.6 .4 2.6 .9 1.6 1.2 1.3 2.6 1.2 1.3 1.5 .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 .9 3.6 4.1 7.2 3.5 3.5 4.5 5.3 6.0 4.7 5.1 8.3 5.8 6.7 4.5 5.7 8.9 4.2 6.6 3.6 3.1 4.2 3.2 6.2 3.0 4.2 4.6 2.0 3.3 7.4 14.5 4.7 3.7 4.0 11.9 14.3 9.6 7.4 9.3 8.8 8.5 9.9 4.5 12.0 4.3 3.0 5.5 3.7 9.5 5.8 6.3 6.6 4.5 9.6 7.2 9.9 10.2 3.6 8.4 11.3 11.0 13.9 4.3 9.2

Explanation / Answer

We can solve this question using excel easily.

First enter data into excel.

Click on Data -------> Data Analysis --------> Regression ------->

Input

Input Y Range : select All commodities values

Input X Range :select values of Food , Shelter , Apparel and Fuel Oil

Output Range : select any empty cell

---------> ok

We get

So the regression equation is

All commodities = - 1.0590 + 0.4753*Food + 0.2495*Shelter - 0.0084*Apparel + 0.2721 * Fuel Oil

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.0590 0.389911 -2.71609 0.015936 -1.89011 -0.22796 -1.89011 -0.22796 Food 0.4753 0.062879 7.559373 1.72E-06 0.341303 0.60935 0.341303 0.60935 Shelter 0.2495 0.100547 2.481608 0.025411 0.035207 0.463829 0.035207 0.463829 Apparel -0.0084 0.16262 -0.0515 0.959604 -0.35499 0.338241 -0.35499 0.338241 Fuel Oil 0.2721 0.115423 2.357519 0.032401 0.026094 0.518129 0.026094 0.518129

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