Chapter 6 of Bradbury (2007), a book on baseball, uses regression analysis to co

Question

Chapter 6 of Bradbury (2007), a book on baseball, uses regression analysis to compare the success of the 30 Major League Baseball teams. For example, the author considers the relationship between xi, market size (i.e., the population in millions of the city associated with each team) and Yi, the number of times team i made the post-season playoffs in the mi=10 seasons between 1995 and 2004.

The author found that “it is hard to find much correlation between market size and ... success in making the playoffs. The relationship ... is quite weak.” The data is plotted in Figure 8.16 and it can be found on http://www.stat.tamu.edu/~sheather/book/docs/datasets/playoffs.txt. The output below provides the analysis implied by the author’s comments.

(a) Describe in detail two major concerns that potentially threaten the validity of the analysis implied by the author’s comments.

(b) Using an analysis which is appropriate for the data, show that there is very strong evidence of a relationship between Y and x.

8.3 Exercises 1. Chapter 6 of Bradbury (2007), a book on baseball, uses regression analysis to compare the success of the 30 Major League Baseball teams. For example, the author considers the relationship between x, market size (i.e., the population in millions of the city associated with each team) and Y, the number of times team I made the post-season playoffs in the m,=10 seasons between 1995 and 2004.

Explanation / Answer

a)

The two major concerns that the author has implied over here are

1)

That there is not much correlation between market size and ... success in making the playoffs.

2)

The relationship is quite week.

b)

Adding a explanatory variable might help in predicting the playoff appearances to a greater extent. For example, adding AverageWins helps in predicting to a greater extent. Please see below the output: -

SUMMARY OUTPUT Regression Statistics Multiple R 0.900313731 R Square 0.810564814 Adjusted R Square 0.796532578 Standard Error 1.209971056 Observations 30 ANOVA df SS MS F Significance F Regression 2 169.1378578 84.56892891 57.76447981 1.76084E-10 Residual 27 39.52880885 1.464029957 Total 29 208.6666667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -21.51184555 2.305978523 -9.328727622 6.16994E-10 -26.24332265 -16.78036844 Population -0.02805575 0.053606878 -0.523361019 0.604992318 -0.138047978 0.081936477 AverageWins 0.304358426 0.029816757 10.20763007 9.11937E-11 0.243179494 0.365537358

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