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Formulas: Regression Coefficient Confidence Interval

Regression Coefficient Confidence Interval Formulas

Below you will find descriptions and details for the 5 formulas that are used to compute confidence intervals for regression coefficients.

Beta function:
Beta function formula
Confidence interval for a regression coefficient:
Confidence interval for a regression coefficient formula
where βj is the value of the regression coefficient for independent variable j, α is the desired confidence interval percentage, SEβj is the standard error for βj, t is a t-value, 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.
t-distribution cumulative distribution function (CDF):
t-distribution cumulative distribution function (CDF) formula
where v is the degrees of freedom, t is the upper limit of integration, and I is the regularized lower incomplete beta function.
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