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Question
NARRBEGIN: SA_82_90The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal "sized stores is selected, with the following results:
| Store | Shelf Space X | Weekly Sales Y |
| 1 | 10 | 2.0 |
| 2 | 10 | 2.6 |
| 3 | 10 | 1.8 |
| 4 | 15 | 2.3 |
| 5 | 15 | 2.8 |
| 6 | 15 | 3.0 |
| 7 | 20 | 2.7 |
| 8 | 20 | 3.1 |
| 9 | 20 | 3.2 |
| 10 | 25 | 3.0 |
| 11 | 25 | 3.3 |
| 12 | 25 | 3.5 |
(A) Draw a scatterplot,of the data and comment on the relationship between shelf space and weekly sales.
(B) Run a regression on this data set and report the results.
(C) What are the least squares regression coefficients of the Y-intercept (a)and slope (b)?
(D) Interpret the meaning of the slope b.
(E) Predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.
(F) Why would it not be appropriate to predict the average weekly sales (in hundreds of dollars) of international food for stores with 35 feet of shelf space for international food?
(G) Identify the coefficient of determination,
, and interpret its meaning.(H) Determine the standard error of the estimate. What does it represent?
(I) Draw a scatterplot of residuals versus fitted values. What does this graph indicate?
Answer
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