About
<math>R^2</math> is an accuracy statistics in order to assess a regression model. It's a summary of the model.
<math>R^2</math> 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.
Articles Related
Formula
<MATH> \begin{array}{rrl} R^2 & = & 1 - \frac{\href{RSS}{RSS}}{TSS} \\ TSS & = & \sum^N_{i=0} (y_i - \bar{y})^2 \\ \end{array} </MATH>
- TSS = Total Sum of Squares where <math>y_i</math> is the i-th response and <math>\bar{y}</math> is the average response.