5. Regression Analysis: Demand estimation for branded consumer products:

Demand estimation for brand-name consumer products is made difficult by the fact that managers must rely on propriety data. There simply is not any publicly available data which can be used to estimate demand elasticities for brand-name orange, frozen entrees, pies, and the like, and with good reason. Competitors would be delighted to know profit margins across a broad array of competing products so that advertising, pricing policy, and product development strategy could all be targeted for maximum benefit. Product demand information is valuable, and jealously guarded.

To consider the process that might be undertaken to develop a better understanding of product demand conditions, consider the example of De Vries Foods Ltd based in Brussels. In early 2023, the company's management initiated an empirical estimation of demand for its deluxe frozen fruit pies. The company is formulating pricing and promotional plans for the coming year, and management is interested in learning how pricing and promotional decisions might affect sales. The company has been marketing frozen fruit pies for several years, and its market research department has collected quarterly data over two years for its main marketing areas in Belgium, including sales quantity, the retail price charged for the pies for several years, local advertising and promotional expenditures, and the price charged by a major competing brand of frozen fruit pies. Statistical data was made available by a Brussels based marketing company provided data on population and disposable income in the De Vries Ltd main market areas, divided into three segments. It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand.

The following regression equation was fit to the data shown in the excel file.

Q = bo+b1P+b2A+b3PX+b4Y+b5Pop+b6T+ u

Q is the quantity of frozen fruit pies sold during a quarter, P is the retail price in euro cents of the company's frozen pies, A represents euro (in thousands) spent on advertising and promotional activities, PX is the price charged in euro cents for competing pies, Y is thousands of euro of disposable income per household, Pop is the population of each zone in the market area (in thousands of persons), T is the trend factor 2021-1=1,...., 2022-4=8), and u is a residual term.

(i) Estimate the regression model for each of the three segments. (ii) Describe the statistical significance of each individual independent variables included in the frozen fruit pie demand equation. (iii) Interpret the coefficient determination, R, for the demand equation. (iv) Interpret the F-test and explain its significance in this case. What is the expected value of the next quarter's unit sales in the market area in Segment C?

Year- Unit Price Advertising Competitor's Income Population Time Quarter Sales (cents) expnditure price (000euro) (000thous) (000euro) Segment A 2022-4 27,500 550 10 375 41.5 2,659 2022-3 25,000 600 7.5 375 40.5 2,500 2022-2 25,000 575 10 375 40 2,450 2022-1 27,500 575 5 400 39.5 2,350 2021-4 22,500 525 10 400 39.5 2,300 2021-3 22,500 500 7.5 325 39 2,250 2021-2 25,000 525 7.5 375 39.5 2,150 2021-1 22,500 600 5 425 39.5 2,150 Segment B 2022-4 27,500 600 5 425 40 2,300 2022-3 25,000 600 5 400 39.5 2,300 2022-2 27,500 525 10 425 39.5 2,250 2022-1 25,000 550 5 400 39 2,200 2021-4 22,500 600 5 400 39 2,250 2021-3 22,500 550 5 375 39 2,200 2021-2 22,500 625 5 400 39 2,200 2021-1 22,500 600 7.5 400 38.5 2,150 Segment C 2022-4 32,500 600 5 400 46 6,200 2022-3 32,500 550 15 375 45.5 6,150 2022-2 27,500 600 5 375 45 6,100 2022-1 22,500 600 10 350 44.5 6,150 2021-4 30,000 550 5 375 45 6,200 2021-3 30,000 575 15 350 44.5 6,250 2021-2 25,000 600 5 450 44.5 6,100 2021-1 22,500 575 5 375 44 6,050