sigma2hatepsilonhatbiased: Residual Variance \hat{sigma}_{\hat{\varepsilon} \...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

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

Calculates an estimate of the error variance

\mathbf{E} ≤ft( σ^2 \right) = \hat{σ}_{\hat{\varepsilon}}^{2}

\hat{σ}_{\hat{\varepsilon} \ \textrm{biased}}^{2} = \frac{1}{n} ∑_{i = 1}^{n} ≤ft( \mathbf{y} - \mathbf{X} \boldsymbol{\hat{β}} \right)^2 \\ = \frac{\boldsymbol{\hat{\varepsilon}}^{\prime} \boldsymbol{\hat{\varepsilon}}}{n} \\ = \frac{\mathrm{RSS}}{n}

where \boldsymbol{\hat{\varepsilon}} is the vector of residuals, \mathrm{RSS} is the residual sum of squares, and n is the sample size.

1	sigma2hatepsilonhatbiased(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 estimated residual variance \hat{σ}_{\hat{\varepsilon} \ \textrm{biased}}^{2} .

Ivan Jacob Agaloos Pesigan

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

Other residual variance functions: .sigma2hatepsilonhatbiased(), .sigma2hatepsilonhat(), sigma2hatepsilonhat()

# Simple regression------------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
X <- X[, c(1, ncol(X))]
y <- jeksterslabRdatarepo::wages.matrix[["y"]]
sigma2hatepsilonhatbiased(X = X, y = y)

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
sigma2hatepsilonhatbiased(X = X, y = y)