\f50% 5. Suppose you want to investigate the factors affecting the sales of canned vegetables in a supermarket. To explore the relationship between the weekly sales of canned vegetables (y), the price (x1), advertising expenditure (x.), whether or not it is a store-brand (x, "1" for store brand and "0" for non-store brand), and the amount of shelf space allocated (x.). You hypothesize a model: y = Bo + 8 1x1 + B 2x2 +Boxixit Box3 +Bexs +Box te. Over a 20-week period, observations of y, XI, X_. x; and x: were recorded to estimate the model. The computer output is reported as below. (a) Please write the fitted model based on the computer output. (2 pts) (b) Please find and interpret the adjusted R of this model. (6 pts) (c) When the price is higher, the positive effect of advertising on sales is assumed to be stronger holding other factors fixed. What is the expected sign of B ? (4 pts) d) Is it reasonable to include the quadratic term (x.) in our model? Please test using a = 0.05. (8 pts) (e) If the average weekly sales of store brand are higher than the one of non-store brand holding other factors fixed. What is the expected sign of B4? Please test this theory using a = 0.05. (10 pts) SUMMARY OUTPUT Regression Statistics Multiple R 0.972 R Square 0.946 Adjusted R. Square 0.920 Standard Error 332.357 Joservations 20.000 ANOVA SS F Significance F Regression 6.000 24917533.168 4152922.195 37.596 1. 768E-07 Residual 13.000 1435998.032 110461.387 Total 19.000 26353531.200 Coefficients Standard Error t Stat P-value Lower 9598 Upper 9536 Intercept -4914.855 1716.704 -2.863 0.013 -8623.569 -1206.142 136.878 47.328 2.892 0.013 34.632 239.124 6.907 1.48 8 4.640 0.090 3.691 10.122 XIX -0.159 0.060 -2.667 0.019 -0.288 -0.030 430.630 180 272 2.389 0.033 41.177 820.083 39.269 41.040 0.957 0.356 -49.394 127.931 0.067 0.371 0.181 0. 859 -0. 735 0.869