dot-intercept: Regression Intercept beta_{1}

In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

Description

Derives the intercept β_1 of a linear regression model from the p \times 1 regression slopes ≤ft( \boldsymbol{β}_{2, \cdots, k} \right), the mean of the regressand ≤ft( μ_y \right), and the p \times 1 means of regressors {X}_{2}, {X}_{3}, …, {X}_{k} ≤ft( \boldsymbol{μ}_{\mathbf{X}} \right) .

Usage

.intercept(slopes = NULL, muy = NULL, muX = NULL, X, y)

Arguments

slopes	Numeric vector of length p or p by 1 matrix. p \times 1 column vector of regression slopes ≤ft( \boldsymbol{β}_{2, 3, \cdots, k} = ≤ft\{ β_2, β_3, \cdots, β_k \right\} \right) .
muy	Numeric. Mean of the regressand variable ≤ft( μ_{\mathbf{y}} \right) .
muX	Numeric vector of length p or p by 1 matrix. p \times 1 column vector of means of the regressors {X}_{2}, {X}_{3}, \cdots, {X}_{k} ≤ft( \boldsymbol{μ}_{\mathbf{X}} \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.
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.

Details

The intercept β_1 is given by

β_1 = μ_y - \boldsymbol{μ}_{\mathbf{X}} \boldsymbol{β}_{2, \cdots, k}^{T} .

Value

Returns the intercept β_1 of a linear regression model derived from the means and the slopes ≤ft( \boldsymbol{β}_{2, \cdots, k} \right) .

Author(s)

Ivan Jacob Agaloos Pesigan

See Also

Other parameter functions: .slopesprime(), .slopes(), intercept(), sigma2epsilon(), slopesprime(), slopes()

jeksterslabds/jeksterslabRlinreg documentation built on Jan. 7, 2021, 8:30 a.m.