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Baseball statistics and linear regression to predict wins

Q: Answer the following questions related to linear regression.

Estimate the model that predicts wins from (grand mean centered) runs scored and (grand mean centered) runs allowed. {Note: Grand mean centering was used to aid in the interpretation of the intercept.}

(a) What is the predicted model?
(b) Do the coefficients have the expected signs?
(c) What is the interpretation of the intercept? Does this make sense?
(d) What is the predicted number of wins for the Orioles? The Twins?
(e) How many wins would we expect from a team that scores 10 runs more than the average, but allows 20 runs more than the average?

See attached Word file for a cleaner version of the question. The data is included below in SPSS format, as well as in Excel. The output is attached with the solution. Note that I have included additional variables that may be interesting in their own right. Feel free to explore.


Solution Preview

(a) The predicted model is yhat = 80.98 + (0.085) gmc_rsc - (0.108) gmc_rall.
gmc_rsc is grand mean centered runs scored and similarly, gmc_rall is grand mean centered runs allowed. Grand mean centering aids in the interpretation of the intercept. If we did not center these predictors, the intercept would represent a team that scored zero runs and allowed zero runs, which obviously makes no sense.
(b) Yes. We expect that runs scored would have a positive relationship with wins and that runs allowed would have a negative relationship with wins. An increase in the runs a team scores should increase wins, while allowing more runs ...

Solution Summary

Using baseball statistics and linear regression, models are fit, to predict wins for teams. SPSS and Excel are used as tools to accomplish the task at hand.