dot-Xbetahat: y-hat <=ft( \mathbf{\hat{y}} = \mathbf{X}...

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

Description

Calculates y-hat ≤ft( \mathbf{\hat{y}} \right), that is, the predicted value of \mathbf{y} given \mathbf{X} using

\mathbf{\hat{y}} = \mathbf{X} \boldsymbol{\hat{β}}

where

\boldsymbol{\hat{β}} = ≤ft( \mathbf{X}^{T} \mathbf{X} \right)^{-1} ≤ft( \mathbf{X}^{T} \mathbf{y} \right) .

Usage

1

Arguments

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.

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

If betahat = NULL, the betahat vector is computed using betahat() with X and y as arguments. If betahat is provided, y is not needed.

Value

Returns y-hat ≤ft( \mathbf{\hat{y}} \right).

Author(s)

Ivan Jacob Agaloos Pesigan

References

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

See Also

Other y-hat functions: .Py(), Py(), Xbetahat(), yhat()


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