### Contents/Index

Mean Squared Error

@Coefficient of Determination

The coefficient of determination, denoted $R^2$ or $r^2$, pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

We define it as
$$
R^2 = 1 - \frac{SS_{res}}{SS_{tot}}
$$
where the total sum of squares is given as
$$
SS_{tot} = \sum_i (y_i - \bar{y})^2
$$
and the sum of residuals is given as
$$
SS_{res} = \sum_i (y_i - \hat{y}_i)^2
$$
Here we have that bar/overline means the arithmetic mean, and we have that $\hat{y}_i$ is the modeled/predicted value at index $i$.