vcovhatbetahat: Variance-Covariance Matrix of Estimates of Regression...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

Description Usage Arguments Value Author(s) References See Also Examples

Calculates the variance-covariance matrix of estimates of regression coefficients using

\widehat{\mathrm{cov}} ≤ft( \boldsymbol{\hat{β}} \right) = \hat{σ}_{\varepsilon}^2 ≤ft( \mathbf{X}^{T} \mathbf{X} \right)^{-1}

where \hat{σ}_{\varepsilon}^{2} is the estimate of the error variance σ_{\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.

1	vcovhatbetahat(X, y)

`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.

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

Ivan Jacob Agaloos Pesigan

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

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

# Simple regression------------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
X <- X[, c(1, ncol(X))]
y <- jeksterslabRdatarepo::wages.matrix[["y"]]
vcovhatbetahat(X = X, y = y)

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
vcovhatbetahat(X = X, y = y)