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

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

sehatbetahatbiased(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(), sehatbetahat(), 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"]]
sehatbetahatbiased(X = X, y = y)
#>      sehatbetahat
#> [1,]   0.72641684
#> [2,]   0.01832688

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
sehatbetahatbiased(X = X, y = y)
#>      sehatbetahat
#> [1,]   1.01342097
#> [2,]   0.36376661
#> [3,]   0.50800108
#> [4,]   0.50489888
#> [5,]   0.06575065
#> [6,]   0.01601016