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

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

Estimates coefficients of a linear regression model.

1	betahat(X, y, qr = TRUE)

`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.
`qr`	Logical. If `TRUE`, use QR decomposition when normal equations fail. If `FALSE`, use singular value decompositon when normal equations fail.

Calculates coefficients using the normal equation. When that fails, QR decomposition is used when qr = TRUE or singular value decomposition when qr = FALSE.

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: Inverting the matrix of the normal equations

Wikipedia: QR decomposition

Wikipedia: Singular value decomposition

Wikipedia: Orthogonal decomposition methods

Wikipedia: Design matrix

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

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

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