Coefficient of Determination

What is it?

The coefficient of determination, or $R^2$, is a statistical measure that provides the goodness of fit of a statistical model. It’s most commonly used with Linear Regression models, both in Statistics and Machine Learning.

It takes a value of $0\le R^2\le 1$, with $R^2=0$ being a model that does not explain any Variance of the predicted variable, and $R^2=1$ being a model that explains all Variance.

Beware the bias

Even though a model can have a good $R^2$ score, it can still be overly biased. Remember that $R^2$ does not account for bias (or Overfitting).

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Calculating R squared

To calculate $R^2$, one need to already have developed the model, once it uses the residual of the predictions. Given $RSS$ as the residual sum of squares, and $SST$ as the total sum of squares, one can calculate $R^2$ using:

$$\begin{array}{rl}& R^2=1-\frac{RSS}{SST},\\ & R^2=1-\frac{\sum (y_i-\hat{y}{)}^2}{\sum (y_i-\overline{y}{)}^2}\end{array}$$

Which will result in a percentage, with range $0\le R^2\le 1$.

Variables in R^2

The normal $R^2$ takes only two variables. If more are used in the model, then consider using Adjusted R Squared.