Wine These data give ratings and prices of 257 red and white wines that appeared in Wine Spectator in 2009. For this analysis, we are interested in how the rating given to a wine is associated with its price, and if this association depends on whether it’s a red or white wine.
(a) Plot the natural log of the price on the score given to the wine. Use color-coding or distinct symbols to distinguish red from white wines in the plot. Is the association between price and score dependent on the type of wine?
(b) Fit a multiple regression of log price on the score to the fit of a multiple regression that allows the effect of the score on price to depend on the type of wine, using an interaction. Check whether this model meets the conditions of the MRM, noting any flaws.
(c) Assume for the following test that the model meets the conditions for the MRM. Use the incremental F-test (see Exercise 45) to assess the difference between a simple regression and a model that allows the effect of score to differ for red and white wines. Does the test agree with the t-statistics observed in (b)? Explain any differences.
(d) Refine the model fit in (b) and summarize the results, noting any problems that remain. If problems remain, note how these affect your conclusions.