Parameter Dispersion (Variance-Covariance) Matrix
The
dispersion matrix for the parameter estimates
is the matrix
, where
is the covariance of
and
. The dispersion matrix is calculated according to the formula
where S
2 is the estimated variance, as defined above, and
X and
are the regression matrix and its transpose, respectively.
Significance of the Model (Overall F Statistic)
The
overall F statistic is a statistic for testing the null hypothesis
β1 =
β2 = ... =
βp – 1 = 0. It is defined by the equation:
where
This statistic follows an F distribution with (p-1) and (n-p) degrees of freedom.
p-Value
The p-value is the probability of seeing the value of the F statistic for a given linear regression if the null hypothesis:
β0 = β1 = ... = βp – 1 = 0
is true.
Critical Value
The critical value of the F statistic for a specified significance level, α , is the value, v, of the F statistic such that if the F statistic calculated for the multiple linear regression is greater than v, we reject the hypothesis β1 = β2 = ... = βp – 1 = 0 at the significance level α.