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

Source: R/vcovhat.R

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

vcovhatbetahatbiased(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.

References

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

See also

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

Author

Ivan Jacob Agaloos Pesigan

Examples

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

#>             [,1]          [,2]
#> [1,]  0.52768142 -0.0127413411
#> [2,] -0.01274134  0.0003358744

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

#>              [,1]          [,2]          [,3]         [,4]          [,5]
#> [1,]  1.027022064 -7.735991e-02 -0.0846131979 -0.003602315 -0.0611951523
#> [2,] -0.077359906  1.323261e-01 -0.0087482453  0.016412105  0.0006846205
#> [3,] -0.084613198 -8.748245e-03  0.2580651020 -0.024393100  0.0032580499
#> [4,] -0.003602315  1.641211e-02 -0.0243930997  0.254922876 -0.0012844045
#> [5,] -0.061195152  6.846205e-04  0.0032580499 -0.001284404  0.0043231481
#> [6,] -0.007340509  6.831423e-05  0.0005628159 -0.001303368  0.0001986687
#>               [,6]
#> [1,] -7.340509e-03
#> [2,]  6.831423e-05
#> [3,]  5.628159e-04
#> [4,] -1.303368e-03
#> [5,]  1.986687e-04
#> [6,]  2.563254e-04