# Hat Matrix Diagonal

**Cases which are influential with respect to any of these measures are marked with an asterisk.**

**Hat matrix diagonal**.
We givenecessary and suļ¬cient conditions on the space of design matrix under which thecorresponding Hat matrix elements get desired extreme values.
The hat matrix diagonal element for observation i denoted hi reflects the possible influ-ence of X.
Coefficients unless docoef is false a matrix whose i-th row contains the change in the estimated coefficients which results when the i-th case is dropped from the regression.

We did not call it hatvalues as R contains a built-in function with such a name. The functions dfbetas dffits covratio and cooks. Analysis of elements of the projection hat matrix plays an important role in regression diagnostics because the diagonal elements of this matrix Hii xi XTX 1 xTi indicate the presence of leverage points which are not detected by analysis of residuals.

The hat matrix H is defined in terms of the data matrix X. The hat matrix projection matrix P in econometrics is symmetric idempotent and positive definite. The primary high-level function is influencemeasures which produces a class infl object tabular display showing the DFBETAS for each model variable DFFITS covariance ratios Cooks distances and the diagonal elements of the hat matrix.

Data points that are far from the centroid of the X-space are potentially influentialA measure of the distance between a data point x i and the centroid of the X-space is the data points associated diagonal element h i in the hat matrix. Belsley Kuh and Welsch 1980 propose a cutoff of 2 p n for the diagonal elements of the hat matrix where n is the number of. Using matrix format Y X.

The predicted values ybcan then be written as by X b XXT X 1XT y. J is the jth diagonal element of X TX 1 - Reject H0 if p-value or jTjT n p 1 1. Model Assessment R Square and MSE.

Properties and Interpretation Week 5 Lecture 1 1 Hat Matrix 11 From Observed to Fitted Values The OLS estimator was found to be given by the p 1 vector b XT X 1XT y. Belsley Kuh and Welsch 1980 propose a cutoff of 2 p nfor the diagonal elements of the hat matrix where nis the. A vector containing the diagonal of the hat matrix.