Calculate MSR, SSR, F-statistic, p-value, R², and adjusted R² from regression sums of squares, degrees of freedom, or observed and predicted values.

Regression ANOVA assumes in-sample ordinary least squares with an intercept. k counts predictors and excludes the intercept; F inference also requires independent, normal errors with constant variance.

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MSR Formula

The following example problem outlines the steps and information needed to calculate the MSR.

MSR = SSR / DOF

Variables:

  • MSR is the mean square of regression (units: response units²).
  • SSR is the regression sum of squares.
  • DOF is the regression degrees of freedom (dfreg = k, the number of predictors; k is an integer).

To calculate the mean square of regression, divide the SSR by the regression degrees of freedom.

How to Calculate MSR?

The following steps outline how to calculate the MSR.

  1. First, determine the SSR. 
  2. Next, determine the regression degrees of freedom (k). 
  3. Next, use the formula from above: MSR = SSR / DOF.
  4. Finally, calculate the MSR.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

SSR = 30

degrees of freedom (k) = 2

MSR = SSR / DOF = 30 / 2 = 15