dot-sigma2hatepsilonhat: Residual Variance \hat{sigma}_{\hat{\varepsilon}}^{2} (from...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

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

Calculates an estimate of the error variance

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

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

where \boldsymbol{\hat{\varepsilon}} is the vector of residuals, \mathrm{RSS} is the residual sum of squares, n is the sample size, and k is the number of regressors including a regressor whose value is 1 for each observation on the first column.

1	.sigma2hatepsilonhat(RSS = NULL, n, k, X, y)

`RSS`	Numeric. Residual sum of squares.
`n`	Integer. Sample size.
`k`	Integer. Number of regressors including a regressor whose value is 1 for each observation on the first column.
`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.