Classic "Oakland A's" Case Study in Statistics - Linear Regressions with Dummy Variables

Problem 3A

Read the “Oakland As (A)” case in the course pack. The data is available in the course website. The tab in the spreadsheet labeled Full Data Set contains the data in Exhibit 1 of the case while the tab labeled Nobel Data contains the attendance figures for the games Nobel pitched in and those he did not pitch in.

(a) Compute the descriptive statistics for the attendance at the games Nobel pitched in and those he did not pitch in. What is the difference in the average attendance for these two sets of games? Does this provide meaningful evidence that Nobel should be paid more because attendance was higher in the games he pitched in?

(b) Plot Ticket against Time (i.e. create a time series plot of Ticket). Do you see any patterns in the data?

(c) Run the regression

Tickett = β0 + β1*Nobelt + εt

where Nobel is a dummy variable that takes the value 1 when Nobel starts on day t.

What are the estimates of β0 and β1? How do these relate to the average attendance figures computed in part (a)?

(d) Do the residuals from the regression in part (c) appear to be independent? Why or why not? If they are not independent, what factors might explain the pattern?

(e) Run the regression

Tickett = β0 + β1Post + β2GBt + β3Tempt + β4Prect + β5TOGt + β6TVt + +β7Promot + β8Nobelt + β9Yankst + β10Weekendt + β11ODt + β12DHt + εt

Do the residuals from this regression appear to be independent? (It is a close call but assume they are independent.) Why would these residuals be independent while the residuals from the model in part (c) are dependent?

(f) What evidence is there about Nobel pitching in a game being related to the attendance at the game? Do you have more confidence in drawing a conclusion from the model in part (c) or the model in part (e) to answer this question? Why?

(g) Do you think Nobel’s agent has a legitimate case that Nobel should be paid more because he brings fans to the games?

Problem 3B

Read the “Oakland As (B)” case in the course packet. The data file is attached to this problem.

(a) Run a regression of Attendance against Wins. What is the interpretation of the coefficient associated with Wins? What is the interpretation of R2 in this regression? What is the practical problem associated with using this model to forecast Attendance for the next season (i.e. to forecast attendance in the 1981 season)?

(b) Now run a regression of Attendance against Roddey’s forecast of the number of wins for that season. Why is the R2 value obtained from this regression so much lower than the R2 obtained from the regression in part (a)?

(c) Why is it more appropriate to use the model in part (b) for forecasting Attendance than the model in part (a)?

(d) Before the 1981 season starts Roddey forecasts 95 wins for the season. Using the model from part (b), what is the prediction for attendance in the 1981 season? What is the standard deviation associated with the prediction?

(e) Using the prediction and standard deviation for the prediction from the model in part (b), what is the probability associated with a bonus to Nobel of $0, $50,000, $100,000 and $150,000? What is the mean of this distribution?

(e) Using the probability distribution from part (d), what is the expected cost if the lump-sum incentive plan is used?