Promotion These data describe spending by a pharmaceutical company to promote a cholesterol lowering drug. The data cover 39 consecutive weeks and isolate the metropolitan areas near Boston,...

Promotion These data describe spending by a pharmaceutical company to promote a cholesterol lowering drug. The data cover 39 consecutive weeks and isolate the metropolitan areas near Boston, Massachusetts, and Portland, Oregon.

The variables in this collection are shares. Marketing research often describes the level of promotion in terms of voice. In place of level of spending, voice is the share of advertising devoted to a specific product. Voice puts spending in context;
10 million might seem like a lot for advertising unless everyone else is spending
200 million. The column Market Share is sales of this product divided by total sales for such drugs in each metropolitan area. The column Detail Voice is the ratio of detailing for this drug to the amount of detailing for all cholesterol-lowering drugs in the metro area. Detailing counts the number of promotional visits made by representatives of a pharmaceutical company to doctors’ offices.

(a) A hasty analyst fit the regression of Market Share on Detail Voice with the data from both locations combined. The analyst found a statistically significant slope for Detail Voice, estimated larger than 1. (This finding implies that a 1% increase in the share of detailing would get on average 1% more of the market.) What mistake has the analyst made?

(b) Propose an alternative model and evaluate whether your alternative model meets the conditions of the MRM so that you can do confidence intervals.

(c) What’s your interpretation of the relationship between detailing and market share? If you can, offer your impression as a range.