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Below you will find descriptions and details for the 9 formulas that are used to compute beta (Type II error rate) values for multiple regression.

Beta function:

Cohen's f^{2} effect size for an F-test:

where

Error function:

F-distribution cumulative distribution function (CDF):

where

Lower incomplete beta function:

Noncentral F-distribution cumulative distribution function (CDF):

where

Noncentral F-distribution noncentrality parameter:

where

Normal distribution cumulative distribution function (CDF):

where

Regularized lower incomplete beta function:

where the numerator is the lower incomplete beta function, and the denominator is the beta function.

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