Py: y-hat <=ft( \mathbf{\hat{y}} = \mathbf{P} \mathbf{y} \right)
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

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

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

\mathbf{\hat{y}} = \mathbf{P} \mathbf{y}

where

\mathbf{P} = \mathbf{X} ≤ft( \mathbf{X}^{T} \mathbf{X} \right)^{-1} \mathbf{X}^{T} .

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

Ivan Jacob Agaloos Pesigan

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

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

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

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