Variance-covariance matrix

A square matrix that contains the variances and covariances associated with several variables. The diagonal elements of the matrix contain the variances of the variables and the off-diagonal elements contain the covariances between all possible pairs of variables.

For example, you create a variance-covariance matrix for three variables X, Y, and Z:

The variances are displayed in bold along the diagonal; the variance of X, Y, and Z are 2.0, 3.4, and 0.82 respectively. The covariance between X and Y is -0.86.

The variance-covariance matrix is symmetric because the covariance between X and Y is the same as the covariance between Y and X. Therefore, the covariance for each pair of variables appears twice in the matrix: the covariance between the ith and jth variables is displayed at positions (i, j) and (j, i).

Many statistical applications calculate the variance-covariance matrix for the estimators of parameters in a statistical model. It is often used to calculate standard errors of estimators or functions of estimators. For example, logistic regression creates this matrix for the estimated coefficients, allowing you to view the variances of coefficients and the covariances between all possible pairs of coefficients.