R-squared • Ben Lau

$R^2 = 1- \frac{residual error}{sum-of-squares from the mean}$ $R^{2} = 1 - \frac{res i d u a l error}{s u m - o f - s q u a res f ro m t h e m e an}$
- residual error is the sum of the squared differences between the observed values and the predicted values
- note that the mean is the horizontal line, which is the simplest model
- It is not always the square of anything, so it can be negative, which means the model is worse than the simplest model
aka coefficient of determination
without the square, it is like the correlation coefficient r
- only if the prediction is a linear regression. In complex models, it is not the same, and there is no r
- ranged from -1 to 1, extremes are good, 0 is bad
- it tells how two quantitative variables are related
Interpretation is easier with the square
It is the percentage of variation explained by the relationship between the two variables