Estimated Regression Intercept $\hat{\beta}_{1}$

.intercepthat(slopeshat = NULL, muyhat = NULL, muXhat = NULL, X, y)

Arguments

slopeshat	Numeric vector of length `p` or `p` by `1` matrix. $p \times 1$ column vector of estimated regression slopes $\left( \boldsymbol{\hat{\beta}}_{2, 3, \cdots, k} = \left\{ \hat{\beta}_2, \hat{\beta}_3, \cdots, \hat{\beta}_k \right\}^{T} \right)$ .
muyhat	Numeirc. Estimated mean of the regressand variable $y$ $\left( \hat{\mu}_y \right)$.
muXhat	Vector of length `p` or `p` by `1` matrix. $p \times 1$ column vector of the estimated means of the regressor variables $X_2, X_3, \cdots, X_k$ $\left( \boldsymbol{\mu}_{\mathbf{X}} = \left\{ \mu_{X_2}, \mu_{X_3}, \cdots, \mu_{X_k} \right\} \right)$.
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.

Value

Returns the estimated intercept $\hat{\beta}_1$ of a linear regression model derived from the estimated means and the slopes $\left( \boldsymbol{\hat{\beta}}_{2, \cdots, k} \right)$ .

Details

The intercept $\beta_1$ is given by $$ \hat{\beta}_1 = \hat{\mu}_y - \boldsymbol{\hat{\mu}}_{\mathbf{X}} \boldsymbol{\hat{\beta}}_{2, \cdots, k}^{T} . $$

Author

Ivan Jacob Agaloos Pesigan

slopeshat	Numeric vector of length `p` or `p` by `1` matrix. \(p \times 1\) column vector of estimated regression slopes \(\left( \boldsymbol{\hat{\beta}}_{2, 3, \cdots, k} = \left\{ \hat{\beta}_2, \hat{\beta}_3, \cdots, \hat{\beta}_k \right\}^{T} \right)\) .
muyhat	Numeirc. Estimated mean of the regressand variable \(y\) \(\left( \hat{\mu}_y \right)\).
muXhat	Vector of length `p` or `p` by `1` matrix. \(p \times 1\) column vector of the estimated means of the regressor variables \(X_2, X_3, \cdots, X_k\) \(\left( \boldsymbol{\mu}_{\mathbf{X}} = \left\{ \mu_{X_2}, \mu_{X_3}, \cdots, \mu_{X_k} \right\} \right)\).
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.

Estimated Regression Intercept \(\hat{\beta}_{1}\)

Arguments

Value

Details

See also

Author