4. (12 points) The product manager for a brand of all-natural herbal shampoo has compiled 15 weeks of data on the weekly sales of the brand (in units), the level of media advertising (in thousands of dollars), the price (in dollars), and the use of displays (in number of stores with the brand on an end-aisle display). She then carried out a multiple regression analysis on these data in order to calculate a price elasticity. Her data and the results of the regression analysis can be seen below. (a) Name each of the variables that were used in this multiple regression analysis. For each of these variables, indicate whether it was an independent variable or a dependent variable in this regression analysis. (b) Use these data and the results of the regression analysis to calculate the price elasticity for this shampoo brand. Show your work. (c) Based on the course material, describe at least two issues that should lead the product manager to not entirely trust the price elasticity calculated from this analysis. Week # 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sales 6320 6522 6896 6404 6572 6897 6356 5816 5945 6236 6345 6572 6897 6534 5816 64085 Advertising 172 185 184 159 163 176 167 157 168 156 172 185 188 159 153 169.6 Price 2.59 2.69 2.39 2.69 2.69 2.39 2.69 3.19 2.99 2.89 2.59 2.59 2.49 2.69 2.89 2.7 Display 81 74 54 65 45 65 57 59 58 56 54 65 45 65 57 60.0 NILI Mean SUMMARY OUTPUT Recresson Statistics Multiple R 0.92 R Square 085 Adjusted R Square 0.81 Standard Error 15542 Observations 15.00 ANOVA df 300 11.00 14.00 Regression Residual Total SS MS 1492659 25 497553.08 265 700.49 24154.59 1758359.73 F 2060 Signdicance F 0.00 Intercept Advertising Price Display Coefficients Standard Error 9328 86 1402 29 5.06 4.80 128605 259.75 -5.18 4.33 Star P-value 6.65 0.00 1.06 0.31 -4.95 0.00 - 1.20 026 Lower 95% Upper 95% ower 95 09/poer 95.02 624243 1241528 6242 43 12415 28 -5.50 15.62 550 15.62 -1857.76 -714.35 -1857 76 -714 35 -14.71 4.34 - 14.71 4.34