Promotion of a new product, simple and multiple regression analysis. (Chapter Appendix, S. Stickel, adapted) “What does all this mean. All I really want to know is whether I should advertise or not, and where?” said Rick Savalas, the sales manager of Cleanhair Products Inc. Rick has asked for your help to understand the results of regression analyses that have been prepared by his assistants for a new product, Glowbright, that Cleanhair Products recently introduced. The notation used is as follows:

y estimated sales of Glowbright Xj dollars incurred on discount coupons placed in magazines X2 dollars spent on advertising Glowbright on television Standard errors ofthe coefficients (not t-statistics) are in parentheses.

1. y = $457,200 + $4.78 Xj r2 = 0.47

($2.08)

2. y = $560,400 + $5.08 X2 r2 = 0.53

($2.23)

3. y = $902,760 + $1.04 X, + $1.09X2 r2 = 0.88

($0.95) ($1.19)

Required 1. For each of the regressions, perform a statistical test and indicate whether sales are affected by discount coupons and television advertising.

2. Contrast the multiple regression results (equation 3) with the simple regression results (equations 1 and 2) in terms of the statistical tests that you performed in requirement 1. Suggest a possible explanation for any differences in the results of the statistical tests.

3. Interpret the $4.78, the $5.08, the $1.04, and the $1.09 coefficients in the regression equations. Specifically, explain briefly what the coefficients imply about whether and how Rick should advertise.