   # In exercise 1, the following estimated regression equation based on 10 observations was presented. ŷ = 29.1270 + .5906 x 1 + .4980 x 2 The values of SST and SSR are 6724.125 and 6216.375, respectively. a. a Find SSE. b. Compute R 2 . c. Compute R a 2 . d. Comment on the goodness of fit. ### Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435

#### Solutions

Chapter
Section ### Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435
Chapter 15.3, Problem 11E
Textbook Problem
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## In exercise 1, the following estimated regression equation based on 10 observations was presented.ŷ = 29.1270 + .5906x1 + .4980x2The values of SST and SSR are 6724.125 and 6216.375, respectively. a. a Find SSE. b. Compute R2. c. Compute R a 2 . d. Comment on the goodness of fit.

a.

To determine

Compute the SSE.

### Explanation of Solution

Calculation:

The regression equation based on 10 observation for independent variables x1, x2 and dependent variable y is y^=29.1270+0.5906x1+0.4980x2. The total sum of squares is SST=6,724.125 and sum of squares due to regression is SSR=6,216.375.

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

Compute R2 for given estimated regression equation.

c.

To determine

Find Ra2.

d.

To determine

Comment on the goodness of fit

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