Influential wine critics such as Robert Parker publish their personal ratings of wines, and many consumers pay close attention. Do these ratings affect the price? The data in this exercise are a sample of ratings and prices found online at the Web site of an Internet wine merchant.
(a) Does the scatterplot of the price of wine on the rating suggest a linear or nonlinear relationship?
(b) Fit a linear regression equation to the data, regressing price on the rating. Does this fitted model make substantive sense?
(c) Create a scatterplot for the log of the price on the rating. Does the relationship seem more suited to regression?
(d) Fit a regression of the log of price on the rating. Does this model provide a better description of the pattern in the data?
(e) Compare the fit of the two models to the data. Can you rely on summary statistics like r2 and se?