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)