What it measures
R squared, the coefficient of determination, reports the fraction of the variance in the target that the model explains. It compares the model error against the error of a baseline that always predicts the mean.
- One means the model explains all the variance.
- Zero means it does no better than predicting the mean.
- Below zero means it does worse than that baseline.
How to read it
R squared is unitless, which makes it handy for comparing models on the same dataset. Unlike RMSE it does not carry the scale of the target, so a value of point eight reads the same whether you predict dollars or grams.
Cautions
R squared has traps. Adding any feature can only raise it on training data, even a useless one, so it rewards complexity. Adjusted R squared counters this by penalizing extra features. R squared also says nothing about whether predictions are biased or whether the model fits a curved relationship, so always pair it with a residual plot.
Key idea
R squared reports the fraction of target variance the model explains versus a mean baseline, and adjusted R squared corrects its bias toward rewarding extra features.