Return to Exercise 1.7, which gave data on advertising impressions retained and advertising expenditure for a sample of 21 firms. In Exercise 5.11 you were asked to plot these data and decide on an appropriate model about the relationship between impressions and advertising expenditure. Letting Y represent impressions retained and X the advertising expenditure, the following regressions were obtained:

a. Interpret both models.
b. Which is a better model? Why?
c. Which statistical test(s) would you use to choose between the two models?
d. Are there €œdiminishing returns€ to advertising expenditure, that is, after a certain level of advertising expenditure (the saturation level), does it not pay to advertise? Can you find out what that level of expenditure might be? Show the necessary calculations.

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Model I: Ý, = 22.163 + 0.3631X; se = (7.089) (0.0971) Î; = 7.059 + 1.0847X; – 0.0040X? = 9.986) (0.3699) p2 = 0.424 Model II: R² = 0.53 (0.0019)