MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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All Greens is a franchise store that sells house plants and lawn and garden supplies. Although All Greens is a franchise, each store is owned and managed by private individuals. Some friends have asked you to go into business with them to open a new All Greens store in the suburbs of San Diego. The national franchise headquarters sent you the following information at your request. These data are about 27 All Greens stores in California. Each of the 27 stores has been doing very well, and you would like to use the information to help set up your own new store. The variables for which we have data are detailed below.
x1 = annual net sales, in thousands of dollars
x2 = number of square feet of floor display in store, in thousands of square feet
x3 = value of store inventory, in thousands of dollars
x4 = amount spent on local advertising, in thousands of dollars
x5 = size of sales district, in thousands of families
x6 = number of competing or similar stores in sales district
x2 = number of square feet of floor display in store, in thousands of square feet
x3 = value of store inventory, in thousands of dollars
x4 = amount spent on local advertising, in thousands of dollars
x5 = size of sales district, in thousands of families
x6 = number of competing or similar stores in sales district
A sales district was defined to be the region within a 5 mile radius of an All Greens store.
| x1 | x2 | x3 | x4 | x5 | x6 |
| 231 | 3 | 294 | 8.2 | 8.2 | 11 |
| 156 | 2.2 | 232 | 6.9 | 4.1 | 12 |
| 10 | 0.5 | 149 | 3 | 4.3 | 15 |
| 519 | 5.5 | 600 | 12 | 16.1 | 1 |
| 437 | 4.4 | 567 | 10.6 | 14.1 | 5 |
| 487 | 4.8 | 571 | 11.8 | 12.7 | 4 |
| 299 | 3.1 | 512 | 8.1 | 10.1 | 10 |
| 195 | 2.5 | 347 | 7.7 | 8.4 | 12 |
| 20 | 1.2 | 212 | 3.3 | 2.1 | 15 |
| 68 | 0.6 | 102 | 4.9 | 4.7 | 8 |
| 570 | 5.4 | 788 | 17.4 | 12.3 | 1 |
| 428 | 4.2 | 577 | 10.5 | 14.0 | 7 |
| 464 | 4.7 | 535 | 11.3 | 15.0 | 3 |
| 15 | 0.6 | 163 | 2.5 | 2.5 | 14 |
| 65 | 1.2 | 168 | 4.7 | 3.3 | 11 |
| 98 | 1.6 | 151 | 4.6 | 2.7 | 10 |
| 398 | 4.3 | 342 | 5.5 | 16.0 | 4 |
| 161 | 2.6 | 196 | 7.2 | 6.3 | 13 |
| 397 | 3.8 | 453 | 10.4 | 13.9 | 7 |
| 497 | 5.3 | 518 | 11.5 | 16.3 | 1 |
| 528 | 5.6 | 615 | 12.3 | 16.0 | 0 |
| 99 | 0.8 | 278 | 2.8 | 6.5 | 14 |
| 0.5 | 1.1 | 142 | 3.1 | 1.6 | 12 |
| 347 | 3.6 | 461 | 9.6 | 11.3 | 6 |
| 341 | 3.5 | 382 | 9.8 | 11.5 | 5 |
| 507 | 5.1 | 590 | 12.0 | 15.7 | 0 |
| 400 | 8.6 | 517 | 7.0 | 12.0 | 8 |
a) Suppose you and your business associates rent a store, get a bank loan to start up your business, and do a little research on the size of your sales district and the number of competing stores in the district. If x2 = 2.8, x3 = 250, x4 = 3.1, x5 = 7.3, and x6 = 2, use a computer to forecast x1 = annual net sales and find an 80% confidence interval for your forecast (if your software produces prediction intervals). (Use 2 decimal places.)
| forecast | |
| lower limit | |
| upper limit |
b) Construct a new regression model with x4 as the response variable and x1, x2, x3, x5, and x6 as explanatory variables. (Use 2 decimal places for the intercept, 4 for x1, 5 for x3, and 3 otherwise.)
| x4 = ______ | _____+ x1 | ______+ x2 | _____+ x3 | _____+ x5 | ____+ x6 |
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