Homework SourseThe marketing manager used shelf space for pet food to predi
The marketing manager used shelf space for pet food to predict weekly sales. For thos data, SSR=20.535 and SST = 30,025.
A) Determine the coefficient of determination, r2, and interpret its meaning. B) Determine the standard error of the estimate. C) How useful do you think this regression model is for predicting sales? Use Excel
Shelf Space
Sales
Aisle Location
5
160
0
5
220
1
5
140
0
10
190
0
10
240
0
10
260
1
15
230
0
15
270
0
15
280
1
20
260
0
20
290
0
20
310
1
| Shelf Space | Sales | Aisle Location |
| 5 | 160 | 0 |
| 5 | 220 | 1 |
| 5 | 140 | 0 |
| 10 | 190 | 0 |
| 10 | 240 | 0 |
| 10 | 260 | 1 |
| 15 | 230 | 0 |
| 15 | 270 | 0 |
| 15 | 280 | 1 |
| 20 | 260 | 0 |
| 20 | 290 | 0 |
| 20 | 310 | 1 |
Solution
Coefficient of determinatin is 0.684. 68.4% of variation in sales is explained by variation in shelf space.
The line of regression is given by
sales = 7.4 shelf space +145
The above line of regression is significant since pvalue of the slope is very low.
Hence the regression model is very useful
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.8270 | |||||||
| R Square | 0.6839 | |||||||
| Adjusted R Square | 0.6523 | |||||||
| Standard Error | 30.8058 | |||||||
| Observations | 12.0000 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1.0000 | 20535.0000 | 20535.0000 | 21.6386 | 0.0009 | |||
| Residual | 10.0000 | 9490.0000 | 949.0000 | |||||
| Total | 11.0000 | 30025.0000 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 145.0000 | 21.7830 | 6.6566 | 0.0001 | 96.4644 | 193.5356 | 96.4644 | 193.5356 |
| Shelf Space | 7.4000 | 1.5908 | 4.6517 | 0.0009 | 3.8555 | 10.9445 | 3.8555 | 10.9445 |
