Regression Models

Regression is a statistics tool that can be used to investigate relationships between variables. The terms "regression" and the general methods for studying relationships now part of this term were introduced by Sir Francis Galton (1822-1911).

Simple Linear Regression

Linear regression attempts to explain the relationship between two independent variables X and Y, with a straight line fit to the data. The ANOVA tables that are shown in Appendix B-1 illustrate the average number of goals scored per game against time and the average number of goals scored per game at lag1 against time. We see that the standard errors for both regressions are high. This suggests that these linear regression models are inappropriate for forecasting purposes. Analysis of the ACF plots was done to examine the error (Appendix B-2). The Durbin-Watson statistic is 0.20, which is significantly less than the corresponding lower bound value found in the statistical tables. This suggests positive correlation of the error terms. From the ACF plots and the Durbin-Watson statistic, we conclude that an auto-correlated regression model based on the independent variables time, games and teams should be used to see if it produces better results.

Auto Regressive Error Model

Referring to Appendix B-3 we get an auto-regressive parameter, AR1 = .933. This suggests a strong correlation with past error terms. The overall conclusion drawn from the findings of the regression models used in Appendix B, is that the linear regression model is not a good representation of a forecasting model. Therefore another statistical model will have to be examined.