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. Formulate the MRM with y given by the Market Share and x given by Detail Voice and Sample Voice.
(a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?
(b) Fit the indicated multiple regression and show a summary of the estimated features of the model.
(c) Does the estimated model appear to meet the conditions for the use of the MRM?
(d) Does this estimated model explain statistically significant variation in the market share?
(e) At a fixed level of sampling, do periods with increased detailing show significantly larger market share?
(f) Does the fit of the multiple regression imply that the pharmaceutical company should no longer invest in detailing and only rely on sampling? Discuss briefy.