These data describe promotional spending by a pharmaceutical company for a cholesterol-lowering drug. The data cover 39 consecutive weeks and isolate the area around Boston. The variables in this collection are shares. Marketing research often describes the level of promotion in terms of voice. In place of the level of spending, voice is the share of advertising devoted to a specific product. The column Market Share is sales of this product divided by total sales for such drugs in the Boston area. The column Detail Voice is the ratio of detailing for this drug to the amount of detailing for all cholesterol-lowering drugs in Boston. Detailing counts the number of promotional visits made by representatives of a pharmaceutical company to doctors’ offices. Similarly, Sample Voice is the share of samples in this market that are from this manufacturer.
(a) Do any of these variables have linear patterns over time? Use timeplots of each one to see. (A scatterplot matrix becomes particularly useful.) Do any weeks stand out as unusual?
(b) Fit the multiple regression of Market Share on three explanatory variables: Detail Voice, Sample Voice, and Week (which is a simple time trend, numbering the weeks of the study from 1 to 39). Does the multiple regression, taken as a whole, explain statistically significant variation in the response?
(c) Does collinearity affect the estimated effects of these explanatory variables in the estimated equation? In particular, do the partial effects create a different sense of importance from what is suggested by marginal effects?
(d) Which explanatory variable has the largest VIF?
(e) What is your substantive interpretation of the fitted equation? Take into account collinearity and statistical significance.
(f) Should both of the explanatory variables that are not statistically significant be removed from the model at the same time? Explain why doing this would not be such a good idea, in general.