Problem: The March 1, 1984 issue of the Wall Street Journal published data which relate to the advertising budget (in millions of dollars) of 21 firms for 1983 and millions of impressions retained per week by the viewers of the products of these firms. The data are based on a survey of 4000 adults in which users of the products were asked to cite a commercial they had seen for the product category in the past week. Letting Y represent impressions retained and X the advertising expenditure, the following regressions were obtained:
Model I:
Yˆi = 22.163 + 0.3631 Xi
se = (7.089) (0.0971) and R-squared=0.424
Model II:
Yˆi = 7.059 + 1.0847 Xi - 0.0040 Xi2
se = (9.986) (0.3699) (0.0019) and R-squared=0.53
1) Interpret both models.
2) Which is a better model? Why?
3) Are there “diminishing returns” to the advertising expenditure, that is, after a certain level of advertising expenditure (the saturation level) it does not pay to advertise? Can you find out what that level of expenditure might be? Show calculations, if any.