Business Analysis Module User’s Guide : Chapter 3 Definitions : Multiple Linear Regression : Significance of Predictor Variables
Significance of Predictor Variables
Let be the estimate for element j of the parameter vector β. The T statistic for the parameter estimate is a statistic for testing the hypothesis that
It is calculated according to the formula:
where is the jth diagonal element of the dispersion matrix. This statistic is assumed to follow a T distribution with np degrees of freedom.
p-Values
The p-value for each parameter estimate is the probability of seeing the value of the calculated parameter using the formula in “Significance of Predictor Variables” if the hypothesis βj = 0 is true.
Critical Values
The critical value of a parameter T statistic for a given level of significance α is the value vj, such that if the absolute value of the T statistic calculated for a given parameter is greater than vj, we reject the hypothesis βj = 0 at the significance level α.