Regression Coefficient Confidence Interval Formulas

Regression Coefficient Confidence Interval Formulas

Below you will find descriptions and details for the 5 formulas that are used to compute the confidence interval for a regression coefficient.

Beta function:

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

Variable definitions:
v = degrees of freedom
t = upper limit of integration
I = regularized lower incomplete beta function

Lower incomplete beta function:

Regression coefficient confidence interval:

Variable definitions:
β_j = value of the regression coefficient for independent variable j
α = desired confidence interval percentage
SE_{β_j} = standard error for β_j
t = a t-value
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