LP Corporation wants to better manage its inventory and profit projections and wants you to develop a model to predict sales of its top-selling allergy product. You gathered sales data for the product over the last twenty months. You determined that sales (measured in millions of bottles) are a function of the selling price (in dollars) per bottle (SP), the advertising expenditure, in millions of dollars, to promote the product (AD) and the effectiveness of its advertising strategy: TV commercials (11 = 1) or Other advertisements (11 = 0). You recommend a second-order model with interaction to predict sales. The Excel output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.9505 R Square 0.9034 Adjusted R Square 0.8588 Standard Error 0.4055 Observations 20 ANOVA Significance df SS MS F F Regression 6 19.9852 5 3309 20.2546 0.0000 Residual 13 2.1379 0.1645 Total 19 22.1231 Standard Coefficients Error t Stat P-value Intercept -253.7600 286.8206 0.8847 0.3924 SP 71 8522 128 9939 0 5570 0 5870Standard Coefficients Error t Stat P-value Intercept -253.7600 286.8206 0.8847 0.3924 SP 71.8522 128.9939 0.5570 0.5870 AD 39.8418 17.4956 2.2773 0.0403 SP2 -2.8464 15.2180 0.1870 0.8545 AD2 -0.7571 0.4520 1.6750 0.1178 SPXAD -7.9616 3.5988 2.2123 0.0455 I1 1.5130 0.2145 7.0542 0.0000 a) Write the population regression model. b) What is the value of R2 and what does this statistic tell you about the model? c) Why is there a difference between the R2 and the Adjusted R2? d) Is there enough evidence to infer that there is an interaction effect between the selling price and the amount of advertising expenditure at the 5% significance level? e) Are TV commercials more effective than Other advertisements in predicting sales at the 5% significance level? f) Using the regression model, estimate sales if Other advertisements are used in promoting the product, with a selling price of $4.25 per bottle and the advertising expenditure set at $7,250,000