dot-yminusyhat: Residuals <=ft( \boldsymbol{\hat{\varepsilon}} = \mathbf{y} -...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

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

Calculates residuals using

\hat{\varepsilon}_{i} = Y_{i} - \hat{Y}_{i} \\ = Y_{i} - ≤ft( \hat{β}_{1} + \hat{β}_{2} X_{2i} + \hat{β}_{3} X_{3i} + … + \hat{β}_{k} X_{ki} \right) \\ = Y_{i} - \hat{β}_{1} - \hat{β}_{2} X_{2i} - \hat{β}_{3} X_{3i} - … - \hat{β}_{k} X_{ki} .

In matrix form

\boldsymbol{\hat{\varepsilon}} = \mathbf{y} - \mathbf{\hat{y}} \\ = \mathbf{y} - \mathbf{X} \boldsymbol{\hat{β}} .

1	.yminusyhat(y, yhat = NULL, X = NULL, betahat = NULL)

`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.
`yhat`	Numeric vector of length `n` or `n` by `1` numeric matrix. n \times 1 vector of predicted values of \mathbf{y} ≤ft( \mathbf{\hat{y}} \right).
`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.
`betahat`	Numeric vector of length `k` or `k` by `1` matrix. The vector \boldsymbol{\hat{β}} is a k \times 1 vector of estimates of k unknown regression coefficients.

If yhat = NULL, the yhat vector is computed using Xbetahat() with X as a required argument and betahat as an optional argument. If yhat is provided, X and betahat are not needed.

Returns an n \times 1 matrix of residuals ≤ft( \boldsymbol{\hat{\varepsilon}} \right), that is, the difference between the observed ≤ft( \mathbf{y} \right) and predicted ≤ft( \mathbf{\hat{y}} \right) values of the regressand variable ≤ft( \boldsymbol{\hat{\varepsilon}} = \mathbf{y} - \mathbf{\hat{y}} \right).

Ivan Jacob Agaloos Pesigan

Wikipedia: Errors and Residuals

Other residuals functions: .My(), .tepsilonhat(), My(), epsilonhat(), tepsilonhat(), yminusyhat()