R-Squared

In Linear Regression is tells us how much of the total Variance of the target outcome is explained by the model.

R2=1−∑i=1n(y(i)−y^(i))2∑i=1n(y(i)−yˉ)2R^2=1-\frac{\sum_{i=1}^n\left(y^{(i)}-\hat{y}^{(i)}\right)^2}{\sum_{i=1}^n\left(y^{(i)}-\bar{y}\right)^2}
  • <0<0 → worse than mean predictor
  • 00 → mean predictor
  • 11 → best possible score.

Adjusted

Normal R-Squared gets bigger with more features, so it is better to use the adjusted version:

Rˉ2=1−(1−R2)n−1n−p−1\bar{R}^2=1-\left(1-R^2\right) \frac{n-1}{n-p-1}

where nn number of datapoints and pp number of features.