Multiple Regression F-Value and p-Value Formulas

Multiple Regression F-Value and p-Value Formulas

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

Beta function:

Cumulative distribution function (CDF) for the F-distribution:

Variable definitions:
d₁ and d₂ = the degrees of freedom
I = regularized lower incomplete beta function

Lower incomplete beta function:

Multiple regression F-value:

Variable definitions:
R² = variance accounted for by the regression model
k = number of predictors in the model
n = total sample size

Regularized lower incomplete beta function:

Variable definitions:
the numerator = lower incomplete beta function
the denominator = beta function