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Coefficient of determination

The coefficient of determination tells how much of the variation in y the regression model explains. With one explanatory variable it is the square of the correlation coefficient. The rest of the variation is noise or factors the model does not capture.

R2=1−∑(yi−y^i)2∑(yi−yˉ)2R^2 = 1 - \frac{\sum (y_i - \hat y_i)^2}{\sum (y_i - \bar y)^2}share of explained variation
R2=r2R^2 = r^2for simple linear regression

Symbols

R2R^2coefficient of determination
y^i\hat y_imodel value
yiy_imeasured value

Example

r=0.9r = 0.9 gives R2=0.81R^2 = 0.81:

the model explains 81 % of the variation.

A high R² does not mean the model is right. Always look at the plot of the residuals too.
Practise regression and correlation for free →

← Correlation coefficient

Part of Statistics and Risk Analysis: Regression and correlation.