dot-slopeshat: Estimates of Regression Slopes \boldsymbol{\hat{beta}}_{2,...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

Description Usage Arguments Details Value Author(s) See Also

Estimates of Regression Slopes \boldsymbol{\hat{β}}_{2, \cdots, k}

1	.slopeshat(SigmaXhat = NULL, sigmayXhat = NULL, X, y)

`SigmaXhat`	`p` by `p` numeric matrix. p \times p matrix of estimated variances and covariances between regressor variables X_2, X_3, \cdots, X_k ≤ft( \boldsymbol{\hat{Σ}}_{\mathbf{X}} \right).
`sigmayXhat`	Numeric vector of length `p` or `p` by `1` matrix. p \times 1 vector of estimated covariances between the regressand y variable and regressor variables X_2, X_3, \cdots, X_k ≤ft( \boldsymbol{\hat{σ}}_{\mathbf{y}, \mathbf{X}} = ≤ft\{ \hat{σ}_{y, X_2}, \hat{σ}_{y, X_3}, \cdots, \hat{σ}_{y, X_k} \right\}^{T} \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.
`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.

Estimates of the linear regression slopes are calculated using

\boldsymbol{\hat{β}}_{2, \cdots, k} = \boldsymbol{\hat{Σ}}_{\mathbf{X}}^{T} \boldsymbol{\hat{σ}}_{\mathbf{y}, \mathbf{X}}

where

\boldsymbol{\hat{Σ}}_{\mathbf{X}} is the p \times p covariance matrix of the regressor variables X_2, X_3, \cdots, X_k and
\boldsymbol{\hat{σ}}_{\mathbf{y}, \mathbf{X}} is the p \times 1 column vector of the covariances between the regressand y variable and regressor variables X_2, X_3, \cdots, X_k

Returns the estimated slopes \boldsymbol{\hat{β}}_{2, \cdots, k} of a linear regression model derived from the estimated variance-covariance matrix.

Ivan Jacob Agaloos Pesigan

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