Multivariable Regression
Ku often employs regression as a method of explaining relationships. A simple regression between two variables, say a player's FT rating and a players FT percentage, draws a line between the observations such that the sum of the squared difference between each point and the line is minimized. In other words, it draws a line between a bunch of points to try to explain the relationship between them. Like so.
- Simple Reg.PNG (30.96 KiB) Viewed 1017 times
Summary of Fit Table
Really the only number I'll ever reference in this table is the Adjusted R squared. This number explains how much of the variation in the dependent variable (offensive efficiency) is explained by the independent variables in the model. In the above example, FT rating explains 70% of the variance observed in FT percentage. If the model is good then the remainder of the variance is explained by randomness, however it is often the case that the remaining variation is explained by omitted variables (in this case, maybe strength, stamina, and whether the FT was shot at home). The adjusted R squared is preferable to the R squared because it penalizes the model for including irrelevant variables, whereas the R squared will always increase when you add a new variable, whether relevant or not.
Analysis of Variance Table
The only number you need to worry about here is the F stat. If this number is very small, less than 0.05, than it indicates that the difference explanatory variables included are explaining different things, i.e. the variables aren’t really all just difference manifestations of the same property.
Residuals by Predicted Plot
On occasion I will include a residuals by predicted plot. With this plot we want the pattern of points to look random. If there is any sort of pattern or trend to the points, it suggests skewness of the data or a poorly fit model.
- Residual by predicted.PNG (10.11 KiB) Viewed 1017 times
This is the most important part of the results. This table describes the relationships between the explanatory variables and the dependent variable. This is best explained with an example.
- Variables.PNG (8.42 KiB) Viewed 1017 times
Well, we'll start with that for now.
