dot-betahatsvd: Estimates of Regression Coefficients \boldsymbol{\hat{beta}}...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

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

Estimates coefficients of a linear regression model using Singular Value Decomposition. The data matrix \mathbf{X} is decomposed into

\mathbf{X} = \mathbf{U} \mathbf{Σ} \mathbf{V}^{T} .

Estimates are found by solving

\boldsymbol{\hat{β}} = \mathbf{V} \mathbf{Σ}^{+} \mathbf{U}^{T} \mathbf{y}

where the superscript + indicates the pseudoinverse.

1	.betahatsvd(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 \boldsymbol{\hat{β}}, that is, a k \times 1 vector of estimates of k unknown regression coefficients estimated using ordinary least squares.

Ivan Jacob Agaloos Pesigan

Wikipedia: Linear regression

Wikipedia: Ordinary least squares

Wikipedia: Singular value decomposition

Wikipedia: Orthogonal decomposition methods

Wikipedia: Design matrix

Other beta-hat functions: .betahatnorm(), .betahatqr(), .intercepthat(), .slopeshatprime(), .slopeshat(), betahat(), intercepthat(), slopeshatprime(), slopeshat()

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

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