Baseball: Keri, J. Baseball Between the Numbers. Basic Books (2006) Chapter 5-2

Question

Baseball: Keri, J. Baseball Between the Numbers. Basic Books (2006) Chapter 5-2 of the award-winning book on baseball makes extensive use of multiple regression. For example, since the 30 Major League Baseball tams play 81 home games during the regular season and receive the largest share of their income for the ticket sales associated with these games the author develops a least squares regression model to predict Y, yearly income (in US dollars 2005) from ticket sales for each team from home games each year. Ticket sales data for each team for each of the years from 1997 to 2004 are used to develop a model. Thus there are 240 rows of data. Twelve potential predictor variables are identified as follows: Six predictor variables measure team quality: x_1 = number of games won in current season x_2 = number of games won in previous season. x_3 = dummy variable for playoff appearance in current season. x_4 = dummy variable for playoff appearance in previous season x_5 = number of winning seasons in past ten years x_6 = number of playoff appearances in past ten years Three predictors to measure stadium quality: x_7 = seating capacity x_8 = stadium quality rating x_9 = honeymoon effect Two predictors measure market quality: x_10 = market size x_11 = per-capita income Finally, x_12 = year is included to allow for inflation. The author found that seven of these predictor variables had a statistically significant impact on attendance revenue (i.e. had a t-statistic significant at least at the 10% level) Describe in detail the two major concerns that potentially threaten the validity of the model.

Explanation / Answer

Two major concerns that threat the validation of the model are:

1) Since there are several variables, the value of coeficient of determination will keep increasing and we cannot decide whether the model is appropriate or not

2) If t-statisctics are different from zero but there is no assumption of normality.

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