All Greens is a fmnchise 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 = Ize of sales district, in thousands of families X5 = 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 231 3 294 8.2 8 156 2.2 232 6.9 4. 10 0.5 149 3 4 519 5.5 600 12 437 4.4 567 10.6 487 4.8 571 11.8 299 3.1 512 8.1 195 2.5 347 7.7 8. 20 1.2 212 3.3 2. 68 0.6 102 4.9 4 570 5.4 788 17.4 12 428 4.2 577 10.5 14. 464 4.7 535 11.3 15 15 0.6 163 2.5 2 65 1.2 168 4.7 3. 98 1.6 151 4.6 2. 398 4.3 342 5.5 16. 161 2.6 196 7.2 6. 397 3.8 453 10.4 s\" a: u 3.' >->- >->->- \"05\"\"U1N inmiamm'omioVHJVW''ooioV"5F-'\\ii-F-W"N H .5 13 497 5 3 518 11.5 16. 1 528 5 6 615 12.3 16 O 99 0.8 278 2.8 6. 14 0.5 1.1 142 3.1 1 12 347 3 6 461 9.6 11 6 341 3 5 382 9.8 11. 5 507 5 1 590 12.0 15 O 400 8.6 517 7.0 12.0 8 (a) Generate summary statistics, including the mean and standard deviation of each variable. Compute the coefficient of variation for each variable. (Use 2 decimal places.) X 5 CV X1 % X2 % X3 % X4 % X5 % X5 % Relative to its mean, which variable has the largest spread of data values? Which variable has the least spread of data values relative to its mean? , X1; X3 , X1; X4 ' X3; X4 , X4; X1 (b) For each pair of variables, generate the correlation coefficient r. For all pairs involving x1, compute the corresponding coefficient of determination . (Use 3 decimal places.) 2 X1, X2 x1 , X3 x1, X4 x1, X5 X1, X 6 X2, X3 x21 X4 x2, X5 X2 , *6 *3 , X4 *3 , * 5 X3, X6 x4, X5 *4, X 6 X5, *6 Which variable has the greatest influence on annual net sales? Which variable has the least influence on annual net sales? O X41 X2 X2; X5 o X5; X4 O X51 X2 (c) Perform a regression analysis with x1 as the response variable. Use X2, X3, X4, X5, and x6 as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x1 can be explained by the corresponding variations in X2, X3, X4, X5, and x6 taken together? (Use 1 decimal place.) (d) Write out the regression equation. (Use 2 decimal places for X3 and x6. Use 1 decimal place otherwise.) X4+ *5+ X6 X1 = *2+ *3+ If 11 new competing stores moved into the sales district but the other explanatory variables did not change, what would you expect for the corresponding change in annual net sales? (Use 2 decimal places.) If you increased the local advertising by 1 thousand dollars but the other explanatory variables did not change, what would you expect for the corresponding change in annual net sales? (Use 2 decimal places.) (e) Test each coefficient to determine if it is or is not zero. Use a 5% level of significance. (Use 2 decimal places for t and 3 decimal places for the P-value.) P-value B2 B3 B4 Conclusion We fail to reject all null hypotheses, there is insufficient evidence that all $; differ from 0. We reject all null hypotheses, there is sufficient evidence that all p; differ from 0. We fail to reject all null hypotheses, there is sufficient evidence that all ; differ from 0. We reject all null hypotheses, there is insufficient evidence that all $; differ from 0. (f) 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(g) Construct a new regression model with x4 as the response variable and x1, x , X3, x5, and X6 as explanatory variables. (Use 2 decimal places for the intercept, 4 forxl, 5 for X3, and 3 otherwise.) x4 = + x1 + x2 + X3 + x5 + x5 Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, X3 = 188, X5 = 6.6, and X6 = 10. Use these data to predict x4 (advertising costs) and nd an 80% confidence interval for your prediction. (Use 2 decimal places.) prediction it upper limit lower Ii At the 80% condence level, what range of advertising costs do you think is appropriate for this store? (Round to nearest integer.) lower limit $ upper limit$