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Formulas: F-Value and p-Value for Multiple Regression

F-Value and p-Value for Multiple Regression Formulas

Below you will find descriptions and details for the 5 formulas that are used to compute F-values and p-values for a multiple regression study.

Beta function:
Beta function formula
F-distribution cumulative distribution function (CDF):
F-distribution cumulative distribution function (CDF) formula
where d1 and d2 are the degrees of freedom, and I is the regularized lower incomplete beta function.
F-value for multiple regression:
F-value for multiple regression formula
where R2 is the variance accounted for by the regression model, k is the number of predictors in the model, and n is the total sample size.
Lower incomplete beta function:
Lower incomplete beta function formula
Regularized lower incomplete beta function:
Regularized lower incomplete beta function formula
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
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