Contains regional market data on Jim's Cheesesteak sales and other economic variables. The variables are: Unit Sales (Q), Price (P), Advertising Expenditures (A), Competitors' Price (CP), Income (I), Population (P). Time (T). 1. Regress Sales (dependent variable) linearly versus independent variables P, A, CF, I, P, T. Report your reSults. 2. Based on economic theory, what signs would you expect these coefcients have? Do they have the hypothesized signs? Which of the variables are statistically signicant (different from zero) at the 95 percent condence level? 3. Now use this data to estimate the multiplicative form of this demand model (use the same dependent and independent variables). Report your results. 4. Compare the statistical properties of your multiplicative model with the linear model. Which ts the data better? Explain why. 5. What is your estimate of the price elasticity of demand (P), income elasticity of demand (I), and cross price elasticity of demand (CP) in the multiplicative model? Compare these elasticity estimates with the corresponding elasticities in the linear model when calculated at mean values for each variable. 6. In the multiplicative model perform a statistical test to determine whether demand is elastic, interest rates are a complement good, and if new car sales are a normal good at the 95 percent condence level. 7. Forecast Jim's Steaks sales during a year in which the price (P) is $6.50, Advertising Expenditures (A) is $29,900, Competitors' Price (CP) is $6.70, Income (1) is $52,000, Population (P) is 7,300,000. Time (T) is 9. Derive a 95 percent condence interval around this forecast. 8. Use the demand elasticities from your multiplicative model to analyze the impact of the following management decisions: a) If Jim's Cheesesteak's competitor lowers price by 10 percent how will this impact Jim's sales (percentage change)? To offset this Jim's Steaks strategically cuts price by 2 percent. Does this strategy work? Explain. b) If income increases by 5 percent how will this impact Jim's sales (percentage change)? In percentage terms how much can Jim' s Steaks increase price without lowering sales below previous levels Explain Extra Credit {up to 5 points): Given your sales forecast above there is a 10 percent chance that cheesesteak sales will be less than or equal to what level? (Hint: Use the standard error of the forecast and the fact that the errors are approximately normally distributed)