Methods and formulas for coefficients in General MANOVA

Select the method or formula of your choice.

Coefficient (Coef)

In matrix terms, the formula that calculates the vector of coefficients in the model is:

Term	Description
X	design matrix
Y	response vector

The standard errors of the coefficients for multiple regression are the square roots of the diagonal elements of this matrix:

Term	Description
X	design matrix
X'	transpose of the design matrix
s²	mean square error

Term	Description
	test statistic for the coefficient
	estimated coefficient
	standard error of the estimated coefficient

The two-sided p-value for the null hypothesis that a regression coefficient equals 0 is:

The degrees of freedom are the degrees of freedom for error, as follows:

n – p – 1

Term	Description
	The cumulative distribution function of the t distribution with degrees of freedom equal to the degrees of freedom for error.
t_j	The t statistic for the j^th coefficient.
n	The number of observations in the data set.
p	The sum of the degrees of freedom for the terms. The terms do not include the constant.