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

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

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(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 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(), .yminusyhat(), My(), epsilonhat(), tepsilonhat()

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

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