COVRATIO

Definition

The COVRATIO consider the influence of the $i$-th observation on $\mathrm{Cov}(\hat{\mathbf{\beta }})$

Single Observation

Consider a Multiple Linear Regression model $\mathbf{y}=\mathbf{X}\mathbf{\beta }+\mathbf{ϵ}$ $COVRATI{O}_i=\frac{\det (s_{(i)}^2({\mathbf{X}}_{(i)}^{⊺}{\mathbf{X}}_{(i)}{)}^{-1})}{\det (s^2({\mathbf{X}}^{⊺}\mathbf{X}{)}^{-1})}$

Set of Observations

Consider a Multiple Linear Regression model $\mathbf{y}=\mathbf{X}\mathbf{\beta }+\mathbf{ϵ}$ $COVRATI{O}_K=\frac{\det (s_{(K)}^2({\mathbf{X}}_{(K)}^{⊺}{\mathbf{X}}_{(K)}{)}^{-1})}{\det (s^2({\mathbf{X}}^{⊺}\mathbf{X}{)}^{-1})}$