# Coefficient of Determination

## Coefficient of Determination

Measure of the quality of the prediction of a linear regression.

This coefficient varies between 0 and 1, between a low predictive power and a high predictive power.

The coefficient of determination (R², the square of the coefficient of the linear correlation r) is an indicator that makes it possible to judge the quality of a simple linear regression. It ensures the alignment between the model and the data observed or to what point the regression equation is suitable to describe the distribution of points.

If R² is zero, this means that the equation of the line of regression determines 0% of the distribution of points.This means that the mathematical model used absolutely does not explain the point distribution.

If R² is equal to 1, this means that the equation of the line of regression is capable of determining 100% of the point distribution. This means that the mathematical model used as well as the parameters a and b calculated are the ones that determine the distribution of points. In short, the closer the coefficient of determination is to 0, the more dispersed the scatterplot is around the line of regression. On the contrary, the closer the R² tends toward 1, the more tightly grouped the points are around the line of regression. When the points are exactly aligned on the line of regression, then R² = 1.

### Notation

The coefficient of determination is noted as .

In the case of a linear correlation, R² = r², where r is the coefficient of the linear correlation.

It should be noted that R² is only the square of the coefficient of correlation r in the specific case of linear regression. In other non-linear regressions (logarithmic, exponential, etc.), this is not the case. To avoid this confusion, we generally note the coefficient of the correlation with a lowercase letter, and the coefficient of determination with a capital letter.