# Statistics - R-squared ($R^2$|Coefficient of determination) for Model Accuracy

$R^2$ is an accuracy statistics in order to assess a regression model. It's a summary of the model.

$R^2$ is the percentage of variance in Y explained by the model, the higher, the better.

The largest r squared is equivalent to the smallest residual sum of squares.

R squared is also known as:

• the fraction of variance explained.
• the sum of squares explained.
• Coefficient of determination

It's a way to compare competing models.

R squared: two same definitions with two different formulations:

• R squares tells us the proportion of variance in the outcome measure that is explained by the predictors
• or The predictor explains (R squared) percentage of the variance in the outcome measure.

If R Squared increases the models get better.

Example by adding multiple predictor if R Squared increased, we say that the model is boosted.

r squared tells the proportion of variance explained by a linear regression model, by a least squares model.

$$\begin{array}{rrl} R^2 & = & 1 - \frac{\href{RSS}{RSS}}{TSS} \\ TSS & = & \sum^N_{i=0} (y_i - \bar{y})^2 \\ \end{array}$$
• TSS = Total Sum of Squares where $y_i$ is the i-th response and $\bar{y}$ is the average response.