The data in Table 5.3 is provided below. Use this data to replicate the results in Table 5.4. Report your results and note any discrepancies with the text.

2.Now use the data from Table 5.3 to estimate a multiplicative demand function for Mrs. Smyth's frozen fruit pies. Report your parameter estimates and regression statistics for the multiplicative model.

a) Describe the statistical significance of each of the independent variables included in the Mrs. Smyth's demand equation. Interpret the coefficient of determination and F statistic for the multiplicative model.

b) Compare the statistical properties of your multiplicative model with the linear model. Which fits the data better? Explain why.

c) In the multiplicative model perform a statistical test to determine whether demand is elastic, your competitor's product is a substitute, and if pies are a normal good at the 95 percent confidence level.

d) What is your estimate of the price elasticity of demand, advertising elasticity of demand, income elasticity of demand, and cross price elasticity of demand in the multiplicative model? Compare these elasticity estimates with the corresponding elasticities in the linear model when calculated at mean values for each variable.

e) Using the linear model, what is the expected value of next quarter's unit sales in the Minneapolis-St. Paul, MN market? Use the value of each independent variable for the last period in the MN market for this forecast. Derive the 95 percent confidence interval for next quarter's actual sales in the Minneapolis- St. Paul market.

Table 5.3

Price Advertising Competitors' Time Year-Quarter Unit Sales (Q) (S) Expenditures ($) Price (9) Income ($) Population Variable Atlanta-Sandy Springs-Marietta, GA 2006-1 193,334 6.90 15,827 7.40 48,421 5,055,856 2006-2 170,041 7.79 20,819 5.18 49,038 5,091,361 2006-3 247,709 6.21 14,062 5.65 49,663 5,127,115 2006-4 183,259 7.29 16,973 6.60 50,296 5,163,120 2007-1 282, 118 6.87 18,815 6.81 50,938 5,199,378 2007-2 203,396 6.46 14,176 5.22 51,587 5,235,891 2007-3 167,447 7.17 17,030 5.59 52,245 5,272,660 2007-4 361,677 5.72 14,456 6.21 52,911 5,309,688 Chicago-Naperville-Joliet, IL-IN-WI 2006-1 401,805 6.57 27,183 5.34 50,456 9,509,448 2006-2 412,312 6.62 27,572 6.56 51,100 9,526,087 2006-3 321,972 7.82 34,367 6.23 51,751 9,542,755 2006-4 445,236 6.57 26,895 6.47 52,411 9,559,452 2007-1 479,713 6.91 30,539 5.75 53,079 9,576,178 2007-2 459,379 6.48 26,679 5.20 53,756 9,592,933 2007-3 444,040 6.44 26,607 5.66 54,441 9,609,718 2007-4 376,046 7.79 32,760 5.23 55,136 9,626,532 Dallas-Fort Worth-Arlington, TX 2006-1 255,203 7.07 19,880 7.46 44,249 5,952,784 2006-2 270,881 6.60 19,151 6.69 44,813 5,986,874 2006-3 330,271 6.07 15,743 6.45 45,385 6,021,160 2006-4 313,485 6.54 17,512 5.44 45,963 6,055,642 2007-1 311,500 6.30 16,984 5.66 46.549 6,090,322 2007-2 370,780 5.81 15,698 6.62 47,143 6,125,200 2007-3 152,338 8.00 22,057 7.43 47,744 6,160,278 2007-4 320,804 6.69 17,460 6.83 48,353 6,195,557 Los Angeles-Long Beach-Santa Ana, CA 2006-1 738, 760 6.21 42,925 5.93 53,929 13,030,242 2006-2 707,015 7.14 50,299 7.20 54,617 13,057,136 2006-3 699,051 5.43 37.364 5.39 55,313 13,084,085 2006-4 628,838 7.30 50,602 4.93 56,018 13,111,090 2007-1 631,934 7.60 53,562 6.26 56,732 13,138,151 2007-2 651,162 7.24 48,911 6.02 57,456 13,165,267 2007-3 765,124 7.06 49,422 7.43 58, 188 13,192,440\f