These data describe spending by a major pharmaceutical company for promoting 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 uses the notion of voice to describe the level of promotion for a product. In place of the absolute spending for advertising, voice is the share of a type of advertising devoted to a specific product. Voice puts this 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 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.
(a) Do timeplots of Market Share and Detail Voice suggest an association between these series? Does either series show simple variation?
(b) Create a scatterplot for Market Share on Detail Voice. Are the variables associated? Does a line summarize any association?
(c) Estimate the least squares linear equation for the regression of Market Share on Detail Voice. Interpret the intercept and slope. Be sure to include the units for each. Note if either estimate represents a large extrapolation and is consequently not reliable.
(d) Interpret r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(e) According to this equation, how does the average share for this product change if the detail voice rises from 0.04 to 0.14 (4% to 14%)?
(f) Plot the residuals from the regression fit in part (c) on the sizes of the files. Does this plot suggest that the residuals possess simple variation?