Variance-Covariance Matrix of Estimates of Regression Coefficients

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(X, y)

Arguments

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.

References

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

Author

Ivan Jacob Agaloos Pesigan

Examples