R-square - Coefficient of Determination

R-square (or R²) is the coefficient of determination.

• NIST

Wikipedia

It measures the amount of linear association between a response variable and explanatory variables.

R² is a test statistic that is used as a part of a hypothesis test. It has a null hypothesis, a null distribution, a critical (rejection) region, and an associated p-value.

The null hypothesis, H0, is that R² = 0.

The alternate hypothesis, Ha, is that R² <> 0.

At an alpha of 0.05, if the p-value < 0.05, then we would reject H0. Otherwise, we would fail to reject H0.

The following is an example of Statistica output showing the R² value along with the results of the the hypothesis test for R².

When there are many explanatory variables or terms in the model, consider using Adjusted R-square instead.

Spurious Correlations

http://www.tylervigen.com/spurious-correlations