In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ŷ = 25 + 10 x 1 + 8 x 2 The data used to develop the model came from a survey of 10 stores; for those data, SST = 16,000 and SSR = 12,000. a. For the estimated regression equation given, compute R 2 . b. Compute R a 2 . c. Does the model appear to explain a large amount of variability in the data? Explain.

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

Solutions

Chapter
Section

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 15.3, Problem 14E
Textbook Problem
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In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given.ŷ = 25 + 10x1 + 8x2The data used to develop the model came from a survey of 10 stores; for those data, SST = 16,000 and SSR = 12,000. a. For the estimated regression equation given, compute R2. b. Compute R a 2 . c. Does the model appear to explain a large amount of variability in the data? Explain.

a.

To determine

Compute R2 for given estimated regression equation.

Explanation of Solution

Calculation:

The regression equation relating sales to inventory investment and advertising expenditures for 10strores is y^=25+10x1+8x2. The total sum of squares is SST=16,000 and sum of squares due to regression is SSR=12,000.

SSE:

The Sum of squares due to error (SSE) is obtained as SSE=i(yiy^i)2 where yi be the observed value of the dependent variable for the i-th observation and y^i be the predicted value of the dependent variable for the i-th observation.

SST:

The total sum of squares (SST) is obtained as SST=i(yiy¯i)2 where yi be the observed value of the dependent variable for the i-th observation and y¯i be the sample mean of the dependent variable for the i-th observation

b.

To determine

Find Ra2

c.

To determine

Explain whether the model appear to explain a large amount of variability in the data.

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