Ozark Bottled Water Products, Inc, hired a marketing consulting firm to perform a test marketing of its new brand of spring water called Liquid Ozarka. The marketing experts selected 15 small and medium-sized towns in Arkansas and Missouri for a one-month-long sales test. For one month, Liquid Ozarka was sold at a variety of prices ranging from $3 per gallon to $4 per gallon, Specifically, in three of the markets, price was set by the marketing experts at $3 per gallon. In three more markets, price was set at $3.25 per gallon, and so on. For each of the 15 market areas, the marketing consultants collected data on average household income (M), the population of the marketing area (N), and the price of a rival brand of bottled water (PR). At the end of the month, total sales of Liquid Ozarka (Q) were tabulated. All relevant data are contained in the data file, "Statistical Project I Data.xIs". Using the above marketing data and the data analysis/regression tool in Excel, estimate the parameters of the linear empirical demand function: Q=a+bP+cM+dPR+eN If any of the parameter estimates are not significant at the 2 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again. 1. What is your estimated linear demand function for Liquid Ozarka (i.e. print your results and write the equation out as above with the estimated coefficients)? 2. How well does the model fit the data? Cite evidence to back your claim? The marketing consultants describe a "typical" market as one in whioh the price of Liquid Ozarka is $3.50 per gallon, average household income is $45,000, the price of rival bottled water is $3 per gallon, and the population is 75,000 . Answer the following questions for this "typical" market scenario. 3. What is the estimated elasticity of demand for Liquid Ozarka? Is demand elastic or inelastic? What percentage would price have to drop to increase sales by 10 percent? 4. What is the estimated income elasticity of demand? Is Liquid Ozarka a normal or inferior good? A 6 percent increase in average household income would be predicted to cause what percentage change in sales of Liquid Ozarka? 5. What is the estimated cross-price elasticity of demand for Liquid Ozarka with respect to changes in price of its rival brand of bottled water? Does the estimated cross-price elasticity have the expected algebraic sign? Why or why not? If the price of the rival brand of water rises by 8 percent, what is the estimated percentage change in sales of Liquid Ozarka? Now use the same data to estimate the parameters for the log-linear empirical demand function: Q=aPbMFPRdNe If any of the parameter estimates are not significant at the 2 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again. 6. What is the estimated log-linear demand function for Liquid Ozarka (i.e. print your results and write the equation out as above with the estimated coefficients)? 7. As a manager, which functional form would you choose (i.e. does a log-linear specification work better than a linear specification of demand for Liquid Ozarka)? Cite evidence to back your claim. 8. Using the estimated log-linear demand function, report the price, income, and crossprice elasticities of demand. How do they compare to the estimated elasticities for the linear demand specification? Ozark Bottled Water Products, Inc, hired a marketing consulting firm to perform a test marketing of its new brand of spring water called Liquid Ozarka. The marketing experts selected 15 small and medium-sized towns in Arkansas and Missouri for a one-month-long sales test. For one month, Liquid Ozarka was sold at a variety of prices ranging from $3 per gallon to $4 per gallon, Specifically, in three of the markets, price was set by the marketing experts at $3 per gallon. In three more markets, price was set at $3.25 per gallon, and so on. For each of the 15 market areas, the marketing consultants collected data on average household income (M), the population of the marketing area (N), and the price of a rival brand of bottled water (PR). At the end of the month, total sales of Liquid Ozarka (Q) were tabulated. All relevant data are contained in the data file, "Statistical Project I Data.xIs". Using the above marketing data and the data analysis/regression tool in Excel, estimate the parameters of the linear empirical demand function: Q=a+bP+cM+dPR+eN If any of the parameter estimates are not significant at the 2 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again. 1. What is your estimated linear demand function for Liquid Ozarka (i.e. print your results and write the equation out as above with the estimated coefficients)? 2. How well does the model fit the data? Cite evidence to back your claim? The marketing consultants describe a "typical" market as one in whioh the price of Liquid Ozarka is $3.50 per gallon, average household income is $45,000, the price of rival bottled water is $3 per gallon, and the population is 75,000 . Answer the following questions for this "typical" market scenario. 3. What is the estimated elasticity of demand for Liquid Ozarka? Is demand elastic or inelastic? What percentage would price have to drop to increase sales by 10 percent? 4. What is the estimated income elasticity of demand? Is Liquid Ozarka a normal or inferior good? A 6 percent increase in average household income would be predicted to cause what percentage change in sales of Liquid Ozarka? 5. What is the estimated cross-price elasticity of demand for Liquid Ozarka with respect to changes in price of its rival brand of bottled water? Does the estimated cross-price elasticity have the expected algebraic sign? Why or why not? If the price of the rival brand of water rises by 8 percent, what is the estimated percentage change in sales of Liquid Ozarka? Now use the same data to estimate the parameters for the log-linear empirical demand function: Q=aPbMFPRdNe If any of the parameter estimates are not significant at the 2 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again. 6. What is the estimated log-linear demand function for Liquid Ozarka (i.e. print your results and write the equation out as above with the estimated coefficients)? 7. As a manager, which functional form would you choose (i.e. does a log-linear specification work better than a linear specification of demand for Liquid Ozarka)? Cite evidence to back your claim. 8. Using the estimated log-linear demand function, report the price, income, and crossprice elasticities of demand. How do they compare to the estimated elasticities for the linear demand specification