Solution on Case Problem 2 (Data_le: WineRatings.csv) of Statistics for Business and Economics, Thirteenth Edition of page 802, Chapter 16,

Case Problem 2Rating Wines from the Piedmont

Region of Italy

Wine Spectatormagazine contains articles and reviews on every aspect of the wine industry, including ratings of wine from around the world. In a recent issue they reviewed and scored

475 wines from the Piedmont region of Italy using a 100-point scale (Wine Spectator,April 30, 2011). The following table shows how the Wine Spectatorscore each wine received is used to rate each wine as being classic, outstanding, very good, good, mediocre, or not recommended.

Score Rating

95-100 Classic: a great wine

90-94 Outstanding: a wine of superior character and style

85-89 Very good: a wine with special qualities

80-84 Good: a solid, well-made wine

75-79 Mediocre: a drinkable wine that may have minor flaws

below 75 Not Recommended

A key question for most consumers is whether paying more for a bottle of wine will result in a better wine. To investigate this question for wines from the Piedmont region we selected a random sample of 100 of the 475 wines thatWine Spectatorreviewed. The data, contained in the file named WineRatings, shows the price ($), theWine Spectatorscore, and the rating for each wine.

Managerial Report

1.Develop a table that shows the number of wines that were classified as classic, outstanding, very good, good, mediocre, and not recommended and the average price. Does there appear to be any relationship between the price of the wine and theWineSpectatorrating? Are there any other aspects of your initial summary of the data that stand out?

2.Develop a scatter diagram with price on the horizontal axis and theWine Spectatorscore on the vertical axis. Does the relationship between price and score appear tobe linear?

3.Using linear regression, develop an estimated regression equation that can be used to predict the score given the price of the wine.

4.Using a second-order model, develop an estimated regression equation that can be used to predict the score given the price of the wine.

5.Compare the results from fitting a linear model and fitting a second-order model.

6.As an alternative to fitting a second-order model, fit a model using the natural logarithm of price as the independent variable. Compare the results with the second order model.

7.Based upon your analysis, would you say that spending more for a bottle of wine will provide a better wine?

8.Suppose that you want to spend a maximum of $30 for a bottle of wine. In this case, will spending closer to your upper limit for price result in a better wine than a much lower price?