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F-ratio = MSM / MSR
Subscripted M means 'Model' and indicates the expected systematic variance. This is often measured as between-measures variation, and the subscript B is consequently often used here.
Subscripted R means 'Residual' and indicates the random, unsystematic variance. This is measured as within-measures variance, and the subscript W is consequently often used.
F can also be calculated with the Pearson correlation coefficient, r:
F = r2 / (1 - r2)(n - 2)
Test statistic = systematic variance / unsystematic variance
This is typically measured as the sum of squares, SS, then this is:
Test statistic = SSM / SSR
However, with multiple variables, there are multiple sums of squares. Therefore the F-ratio takes the mean of these.