The use of regression analysis for demand estimation can be further illustrated by expanding the Electronic Data Processing (EDP), Inc., example described in the chapter. Assume that the link between units sold and personal selling expenditures described in the chapter gives only a partial view of the impact of important independent variables. Potential influences of other important independent variables can be studied in a multiple regression analysis of EDP data on contract sales (Q), personal selling expenses (PSE), advertising expenditures (AD), and average contract price (P). Because of a stagnant national economy, industry-wide growth was halted during the year, and the usually positive effect of income growth on demand was missing. Thus, the trend in national income was not relevant during this period. For simplicity, assume that relevant factors influencing EDP's monthly sales are as follows:

.:.

If a linear relation between unit sales, contract price, advertising, and personal selling expenditures is hypothesized, the EDP regression equation takes the following form:

where Y is the number of contracts sold, P is the average contract price per month, AD is advertising expenditures, PSE is personal selling expenses, and u is a random disturbance term--all measured on a monthly basis over the past year.

When this linear regression model is estimated over the EDP data, the following regression equation is estimated (t-statistics in parentheses):

Where P_t is price, Ad_d is advertising, Pes_t is selling expense, and statistics are indicated within parentheses. The standard error of the estimate or SEE is 123.9 units, the coefficient of determination or R² = 97.0%, the adjusted coefficient of determination is R̅² = 95.8%, and the relevant F statistic is 85.4.

 

A. What is the economic meaning of the b₀ = ‑117.513 intercept term? How would you interpret the value for each independent variable's coefficient estimate?

B. How is the standard error of the estimate (SEE) employed in demand estimation?

C. Describe the meaning of the coefficient of determination, R², and the adjusted coefficient of determination, R̅². 

D. Use the EDP regression model to estimate fitted values for units sold and unexplained residuals for each month during the year.

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Units Sold, Price, Advertising and Personal Selling Expenditures for Electronic Data Processing, Inc. Units Price Advertising Personal Selling Month Sold Expenditures Expenditures January 2,500 S3,800 S26,800 $43,000 February 2,250 3,700 23,500 39,000 March 1,750 3,600 17,400 35,000 April 1,500 3,500 15,300 34,000 May 1,000 3,200 10,400 26,000 June 2,500 3,200 18,400 41,000