In early 2002, Mrs. Smyth's, a Chicago-based food company, initiated an empirical estimation of demand for its gourmet frozen fruit pies. The firm wants to formulate pricing and promotional plans for the future on the basis of historical data, and management is interested in learning how pricing and promotional decisions might affect sales. Mrs. Smyth's has been marketing frozen fruit pies for several years, and its market research department has collected quarterly data over two years for six important marketing areas, including unit sales quantity, the retail price charged for the pies, local advertising and promotional expenditures, and the price charged by a major competing brand of frozen pies. Statistical data published by the U.S. Census Bureau on population and disposable income in each of the six market areas were also available for analysis. It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand. These data appear in the table below.

Run one linear regression of the following form using all these data and report the equation with the estimated coefficients.

Q_it=b₀+b₁P_it+b₂A_it+b₃PX_it+b₄Y_it+b₅Pop_it+b₆T_it

The subscript i indicates the regional market from which the observation was taken, whereas the subscript t represents the quarter during which the observation occurred.

Where:

Q is the quantity of pies sold during the t th quarter

P is the retail price in dollars of Mrs. Smyth's frozen pies

A represents the dollars spent for advertising;

PX is the price, measured in dollars, charged for competing fruit pies

Y is dollars of disposable income per capita

Pop is the population of the market area

T is the trend factor (2000 -1 = 1,..., 2001 -4 = 8)

Unit Advertising Year- Sales Expenditures Competitors' Time Quarter (Q) Price ($) ($) Price ($) Income ($) Population Variable (T) Atlanta, GA 2000-1 193,334 6.39 15,827 6.92 33,337 4,116,250 2000-2 170,041 7.21 20.819 4.84 33,390 4,140,33 2000-3 247,709 5.75 14,062 5.28 33,599 4,218,965 2000-4 183,259 6.75 16,97 6.17 33,797 4,226,07 2001-1 282,118 6.36 18,815 6.36 33,879 4,278,912 2001-2 203,396 5.98 14,176 4.88 34,186 4,359,442 167,447 6.64 17,030 5.22 35,691 4,363,494 2001-4 361,667 5.3 14,456 35,950 4,380,084 Chicago, IL 2000-1 401,805 6.08 27,183 4.99 34,983 9,184,926 Gary, IN 2000-2 412,312 6.13 27,572 6.13 35,804 ,237,683 Kenosha, WI 2000-3 321,972 7.24 34.367 5.82 35.898 9,254, 182 2000-4 445,236 6.08 26,895 6.05 36,113 9,272,758 2001-1 479,713 6.4 30,539 5.3' 36,252 9,300,401 2001-2 459,379 6 26,679 4.86 36,449 ,322,168 2001-3 444,040 5.96 26,607 5.2 37,327 ,323,331 2001-4 376,046 7.21 32,760 4.89 37,841 9,348,725 Dallas-Fort 2000-1 255,203 6.55 19,88 6.97 34,870 5,294,645 Worth, TX 2000-2 270,881 6.11 19,15 6.25 35,464 5,335,816 2000-3 330,271 5.62 15,743 6.03 35,972 5,386, 134 2000-4 313,485 6.06 17,512 5.08 36,843 5,409,350 2001-1 311,500 5.83 16,984 5.29 37,573 5,409,358 2001-2 370,780 5.38 15,698 6.19 37,78 5,425,001 2001-3 152,338 7.41 22,057 6.94 37,854 5,429,300 2001-4 320,804 6.19 17,460 6.38 39,231 5,442,595 Los Angeles- 2000-1 738,760 5.75 42,925 5.54 28,579 16,381,600 . VanA W N N NO V Q UA W N N O V Q UA W N N O V Q UA W N H O V G UA W N - DO VaVAWN Long Beach, CA 2000-2 707,015 6.61 50,299 6.73 28,593 16,544,289 2000-3 699,051 5.03 37,364 5.04 28,633 16,547,258 2000-4 628,838 6.76 50,602 4.61 28,83 16,553,958 2001-1 631,934 7.04 53,562 5.85 29.242 16,587,432 2001-2 651,162 6.7 48.911 5.63 29,876 16,680,782 2001-3 765,124 6.54 49,422 6.94 30,327 16,716,93 2001-4 741,364 5.73 44,061 6.37 30.41 16,717,938 Minneapolis 2000-1 291,773 5.35 13,896 5.78 29,778 2,972,443 St. Paul, MN 2000-2 153,018 6.33 27,429 4.73 30,079 2,974,275 2000-3 574,486 5.94 31,631 30,598 2,989,720 2000-4 75,396 39,176 4.58 30,71 3,020,244 2001-1 590,190 3.19 33,538 5.17 30,922 3,021,618 2001-2 288,112 7.02 53,643 5.15 31.19 3,025,298 2001-3 276,619 7.02 60,284 5.46 31.35 3,042,834 2001-4 522,446 5.23 53,595 6.06 31,42 3,063,011 Washington, DC, 2000-1 395,314 5.8 22,626 6.56 38,892 7,611,304 Baltimore, MD 2000-2 436,103 5.32 22,697 6.38 39,080 7,615,783 2000-3 336,338 6.35 25,475 4.53 39,510 7,666,220 2000-4 451,321 5.95 25, 734 6.31 7,710,368 2001-1 352,181 6.01 23, 777 6.24 39,776 7,713,007 317,322 7.02 27,544 4.86 41,068 7,752,393 2001-3 422,455 5.71 23.852 4.8 47.471 7,754,204 2001-4 290,963 7.36 30,487 5.32 41,989 7,782,654 Average 391,917 6.24 29,204 5 .7 34,750 7,706,365