DSC 330 - Business Statistics

Statistics in Action 2

When is it?

The second for-credit "Statistics in Action" session will be held in class on Wednesday, week 7.

What you need to do

You should prepare for the session which will be based on the situation described below: "Bordeaux Wine." Before class, read the material in the text-book, and get together in your group to discuss the problem. Use the questions listed to guide your discussion. Then, when you come to class you should be prepared to participate in a class-discussion, using what you've already discussed in your group. You can (and probably should) make notes on what you've discussed in your group before class. You should bring these notes to the class-discussion. Do not turn anything in however - this is not a written assignment.

What will happen

Grading for the session will be on a zero/full credit basis. A question about the relevant study will be asked at the beginning of the session, and each group will write their answer down on a piece of paper. This will then be collected (and checked) by the instructor. Then the class discussion will begin. Each member of a group will receive full credit for that session if the group gets their written answer correct, or, if not, if at least one of the group makes some relevant remark in the ensuing discussion. If the group gets their written answer wrong and no-one in the group makes a useful contribution to the discussion, everyone in that group gets zero credit for that session.

In class, after the beginning question, we'll discuss the focus questions and also anything else that comes up that you think is relevant or interesting in the context of the problem. To keep the class-discussion orderly and the grading fair, you must raise your hand before saying something. The instructor will ignore anything you say unless you've raised your hand first and been asked to speak. The instructor will do his best to allow the first person to raise their hand the opportunity to speak each time. If you keep your hand up, you will be given the opportunity to speak once the current speaker has finished making their point.

When you make a relevant observation, suggest a useful approach to answering a question, or raise an interesting question not previously considered, the instructor will make a note of which group you are in, and keep a tally of which groups have participated and which have not. Remember, you only need get the beginning question correct, or, failing that, make one relevant remark to get full credit for your group. The instructor will decide what is relevant and what is not, and his decision is final - no arguments.

The Situation: "Bordeaux Wine"

The vineyards in the Bordeaux region of France are known for producing excellent red wines. However, the uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some Bordeaux vineyards produce better wines than others, encourages speculation concerning the value of a case of wine produced by a certain vineyard during a certain year (or vintage). As a result, many wine experts attempt to to predict the auction price of a case of Bordeaux wine.

The publishers of a newsletter titled Liquid Assets: The International Guide to Fine Wine discussed a multiple regression approach to predicting the London auction price, Y (in dollars), of red Bordeaux wine in Chance (Fall 1995). The natural logarithm of the price, log_e(Y), of a case containing a dozen bottles of red wine was modeled as a function of weather during the growing season and age of vintage using data collected for the vintages of 1952-1980 (excluding 1954 and 1956 vintages because they are now rarely sold). Three models were fit to the data. The results of the regressions are summarized in the following table:

Focus

1. The three models have R² and s values as shown in the table. Based on this information, which of the three models would you use to predict red Bordeaux wine prices? Explain.
2. For the model you selected, conduct a hypothesis test for each of the regression parameters in the model. Interpret the results.
3. When log_e(Y) is used as a response variable, the "antilogarithm" of a regression parameter minus 1, that is exp(b)-1 or e^b-1, represents the proportional change in Y for every 1-unit increase in the associated X value, holding the other predictors fixed (see explanation below). Use this information to interpret the parameter estimates of the model you selected.

Explanation for result used in question 3

1. Take model 2 for example, and write it as log_e(Y) = b₀ + b₁ X₁ + b₂ X₂ + b₃ X₃ + b₄ X₄.
2. Exponentiate both sides to get Y = exp(b₀ + b₁ X₁ + b₂ X₂ + b₃ X₃ + b₄ X₄).
3. If we increase X₁ by one unit, this becomes exp(b₀ + b₁ X₁ + b₁ + b₂ X₂ + b₃ X₃ + b₄ X₄).
4. Take the difference between the expressions in (c) and (b) to get exp(b₀ + b₁ X₁ + b₂ X₂ + b₃ X₃ + b₄ X₄) (exp(b₁) - 1).
5. Express this difference as a proportional change relative to Y before we increased X₁ by one unit: exp(b₁) - 1
6. Multiply by 100 to convert this to a percentage change.