Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 47

Part of the never-ending debate about what makes a winning baseball team is the theory that a team cannot win consistently without good pitching. Baseball is a sport deeply rooted in analytics and there is an ever-growing body of data available. Major league baseball now has a system in all stadiums that includes cameras and other sensors to collect data on every pitch, including pitch speed, player positions, launch angle for balls hit in the air, and so forth. Table B.22 contains a summary of performance for 2016 for all National and American League baseball teams. The response variable is the number of games won and among the various statistics listed is the team earned run average (ERA), a standard measure of pitching performance, with low values of team ERA generally attributed to an outstanding pitching staff. Figure 2.8 is the JMP output from fitting a linear regression model to wins versus the ERA data. The plots of wins versus ERA and actual versus predicted show that there is definitely a linear relationship between these variables. The model is significant and it seems that one point of team ERA is equivalent to about 18.6 wins. JMP also produces a plot of residuals versus the predicted number of wins. Residual plots such as this are useful in assessing model adequacy. We will discuss this in detail later but this plot indicates that there is no structure in the relationship between the residuals and the predicted number of wins. This is one indication that the model fit is satisfactory. However, the model only explains about 63% of the variability in the response. While this is not bad, it does suggest that there may be other useful explanatory variables.

Figure 2.8 JMP output for the model relating team wins to team ERA for the 2016 baseball season.