Variance-Covariance Matrix of Estimates of Regression Coefficients (from \(\hat{\sigma}_{\varepsilon}^{2}\))

Calculates the variance-covariance matrix of estimates of regression coefficients using $$ \widehat{\mathrm{cov}} \left( \boldsymbol{\hat{\beta}} \right) = \hat{\sigma}_{\varepsilon}^2 \left( \mathbf{X}^{T} \mathbf{X} \right)^{-1} $$ where \(\hat{\sigma}_{\varepsilon}^{2}\) is the estimate of the error variance \(\sigma_{\varepsilon}^{2}\) and \(\mathbf{X}\) is the data matrix, that is, an \(n \times k\) matrix of \(n\) observations of \(k\) regressors, which includes a regressor whose value is 1 for each observation on the first column.

.vcovhatbetahat(sigma2hatepsilonhat = NULL, X, y)

Arguments

sigma2hatepsilonhat	Numeric. Estimate of error variance.
X	n by k numeric matrix. The data matrix \(\mathbf{X}\) (also known as design matrix, model matrix or regressor matrix) is an \(n \times k\) matrix of \(n\) observations of \(k\) regressors, which includes a regressor whose value is 1 for each observation on the first column.
y	Numeric vector of length n or n by 1 matrix. The vector \(\mathbf{y}\) is an \(n \times 1\) vector of observations on the regressand variable.

Value

Returns the variance-covariance matrix of estimates of regression coefficients.

Details

If sigma2hatepsilonhat = NULL, sigma2hatepsilonhat is computed using sigma2hatepsilonhat().

References

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

See also

Other variance-covariance of estimates of regression coefficients functions: .vcovhatbetahatbiased(), vcovhatbetahatbiased(), vcovhatbetahat()

Author

Ivan Jacob Agaloos Pesigan