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6. (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 # Sales Advertising Price Display 6320 172 2.59 81 2 652 185 2.69 74 3 6896 184 2.39 4 54 6404 159 2.69 5 65 6572 163 2.69 6 45 6897 76 2.39 65 7 6356 167 .69 57 8 5816 57 3.19 59 5945 68 2.9 58 10 5236 156 11 2.89 56 6345 12 172 2.59 54 657 185 2.59 13 65 6897 188 2.49 14 45 6534 159 2.69 65 15 5816 153 2.89 57 Mean 6408.5 169.6 2.7 60.0 SUMMAR Y OUTPUT Regression Statistics Multiple R 0.92 R Square 0.85 Adjusted R Square 0.81 Standard Error 15 5.42 Observations 15.00 ANOVA df SS MS F Regression 300 1492 659.25 497553.08 Significance F 20.60 0.00 Residual 11.00 265 700.49 24154.59 Total 14.00 1758 359.73 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% ow er 95.09 Jpper 95.0% Intercept 932 8.86 1402.29 6.65 0.0 0 6242.43 12415.28 6242.43 124 15 28 Advertising 5.06 .80 1.06 0.31 5.50 15.62 -5.50 15.62 Price - 128 6.05 259.75 4.95 0.00 -1857.76 -714.35 -1857.76 -714 .35 Display -5.18 4.33 -1.20 0.26 -14.71 4.34 -14.71 4.34