y-hat $\left( \mathbf{\hat{y}} = \mathbf{P} \mathbf{y} \right)$

Calculates y-hat $\left( \mathbf{\hat{y}} \right)$, that is, the predicted value of $\mathbf{y}$ given $\mathbf{X}$ using $$ \mathbf{\hat{y}} = \mathbf{P} \mathbf{y} $$ where $$ \mathbf{P} = \mathbf{X} \left( \mathbf{X}^{T} \mathbf{X} \right)^{-1} \mathbf{X}^{T} . $$

.Py(y, P = NULL, X = NULL)

Arguments

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.
P	`n` by `n` numeric matrix. The $n \times n$ projection matrix $\left( \mathbf{P} \right)$.
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.

Value

Returns y-hat $\left( \mathbf{\hat{y}} \right)$.

Details

If P = NULL, the P matrix is computed using P() with X as its argument. If P is provided, X is not needed.

References

Wikipedia: Linear Regression

Wikipedia: Ordinary Least Squares

Author

Ivan Jacob Agaloos Pesigan

y-hat \(\left( \mathbf{\hat{y}} = \mathbf{P} \mathbf{y} \right)\)

Arguments

Value

Details

References

See also

Author

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.
P	`n` by `n` numeric matrix. The \(n \times n\) projection matrix \(\left( \mathbf{P} \right)\).
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.