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R-square - Coefficient of Determination

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

  • NIST

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