Initial levels of advertising often bring a larger response in the market than later spending. In this example, advertising comes in the form of devoting more shelf space to the indicated product. The level of sales is the weekly total sales of this product at several outlets of a chain of markets. The display space gives the number of shelf feet used to display the item. The data include sales at 48 stores.
(a) Create a scatterplot for the level of sales on the number of shelf feet. Does the relationship appear linear? Do you think that it ought to be linear?
(b) Fit a linear regression equation to the data, regressing sales on the number of shelf feet. Does this fitted model make substantive sense?
(c) Consider a scatterplot that shows sales on the log of the number of shelf feet. Does the relationship seem more linear than in part (a)?
(d) Fit a regression of sales on the log of the number of shelf feet. Does this model provide a better description of the pattern in the data? What do the slope and intercept tell you?
(e) Compare the ft of the two models to the data. Can you rely on summary statistics like r2 and se?