Linear Regression Applied to Major League Baseball

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For major league baseball (MLB), payroll amounts relate to team wins. While introspecting the MLB game phenomenon, Killins (2014) established that there is a strong relationship between payroll and amount and team wins. Applying regression techniques by drawing a scatter plot of real-world data of MLB payroll amounts (independent variable) and win totals (dependent variable) copied to the Excel spreadsheet, it is practical to establish the nature of the relationship between the two variables.

Comparing Least Square and Linear Regression Models

Least square regression is a technique of estimation, which allows analysts to predict the parameters of the models. For example, OLS models are a model applied when estimating the parameters of linear regression models. On the other hand, a linear regression model is a technique applied in joining a set of distributions that satisfy a set of postulations. These models are both used in predicting independent variables.

Scatter Plot and Linear Regression Model

The scatter plot in Figure 1 represents the values of total wins as an independent variable, while MLB payroll amounts are considered dependent. In addition, the chart in Figure 1 displays a linear regression model, which explains the relationship between payroll amounts and total wins, as shown in Equation 1. The model is used in calculating predicted win totals and associated residuals, as indicated in Table 2 (Appendix). The coefficient of correlation squared is provided alongside the linear regression model. To find the correlation coefficient, the analyst obtained the square root of . Undeniably, the correlation coefficient is slightly above 0.5, indicating that there is a fairly strong positive relationship between MLB payroll amounts and total wins.

Assuming the MLB payroll amount is $150 million, we can determine the wins total using Equation 1 as shown in Exhibit 1. The predicted value calculated in Exhibit 1 lies within the range of win totals data points.

Determination of Correlation Coefficient Using Formula

Where x and y represent MLB payroll amounts and wins total, respectively, and n=30. Table1 shows the values of the items in Equation 2, copied from the Excel spreadsheet.

Table 1: Summary of the Items in Equation 2 from the Excel Spreadsheet.

Item Value
x 3964
y 2431
xy 331776
x2 586086
y2 203273

Determining Outliers Points

After fitting a linear regression line and activating data labels as shown in Figure 2, outlies points are far away from the line. There are two points identified, including Rays (50,90) and Orioles (80, 47).

Conclusively, linear regression techniques, especially constructing scatter plots and fitting linear regression lines are useful in solving practical problems. The MLB scenario analyzed, yielded a correlation coefficient of 0.5339 (manually calculated) or 0.5338 (Excel generated). This value is slightly more than 0.5, showing a relatively strong positive relationship between MLB payroll amount and win totals.

Reference

Killins, R. (2017). . Applied Economics Letters, 24(16), 1189-1193. Web.

Appendix

Appendix A: Table 2 Showing Predicted Win Totals and Residuals

MLB Payroll Amounts (Millions $) Win Totals (Millions$) Predicted Win Totals Residuals=Win-Predicted Win
212 95 94.574 0.426
205 100 93.3875 6.6125
204 82 93.218 -11.218
204 108 93.218 14.782
200 73 92.54 -19.54
177 80 88.6415 -8.6415
171 92 87.6245 4.3755
166 103 86.777 16.223
165 88 86.6075 1.3925
153 89 84.5735 4.4265
151 91 84.2345 6.7655
149 77 83.8955 -6.8955
145 80 83.2175 -3.2175
134 67 81.353 -14.353
128 96 80.336 15.664
123 91 79.4885 11.5115
118 90 78.641 11.359
115 78 78.1325 -0.1325
108 82 76.946 5.054
107 67 76.7765 -9.7765
105 64 76.4375 -12.4375
103 58 76.0985 -18.0985
103 97 76.0985 20.9015
91 62 74.0645 -12.0645
80 47 72.2 -25.2
76 82 71.522 10.478
76 66 71.522 -5.522
71 73 70.6745 2.3255
71 63 70.6745 -7.6745
53 90 67.6235 22.3765
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