Standard Errors of Estimates of Regression Coefficients (from \(\hat{\sigma}_{\varepsilon \ \textrm{unbiased}}^{2}\))

Source: R/sehat.R

\(\widehat{\mathbf{se}}\) is equal to the square root of the diagonal elements of \(\widehat{\mathrm{cov}} \left( \boldsymbol{\hat{\beta}} \right)\) .

sehatbetahat(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.

See also

Other standard errors of estimates of regression coefficients functions: .sehatbetahatbiased(), .sehatbetahat(), .sehatslopeshatprimedelta(), .sehatslopeshatprimetb(), sehatbetahatbiased(), sehatslopeshatprimedelta(), sehatslopeshatprimetb()

Author

Ivan Jacob Agaloos Pesigan

Examples

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

#>      sehatbetahat
#> [1,]   0.72698105
#> [2,]   0.01834111

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

#>      sehatbetahat
#> [1,]   1.01578786
#> [2,]   0.36461621
#> [3,]   0.50918754
#> [4,]   0.50607809
#> [5,]   0.06590421
#> [6,]   0.01604756