# 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.