Hat Matrix Linear Models

Some simple properties of the hat matrix are important in interpreting least squares.

Hat matrix linear models. Overview Ordinary Least Squares OLS Distribution Theory. EY i alle Werte aus annehmen dh. It is defined as the matrix that converts values from the observed variable into estimations obtained with the least squares method.

Ist gx x ln kann. I i 1 2 n ˆ. Suppose we have a linear regression model Y Xβe Y X β e.

The hat matrix is a matrix used in regression analysis and analysis of variance. Learn more about hat matrix leverage linear regression fitlm. Frank Wood fwoodstatcolumbiaedu Linear Regression Models Lecture 11 Slide 20 Hat Matrix Puts hat on Y We can also directly express the fitted values in terms of only the X and Y matrices and we can further define H the hat matrix The hat matrix plans an important role in diagnostics for regression analysis.

However they will. Linear model with one predictor variable. Instead CV can be computed after estimating the model once on the complete data set.

The hat matrix H is defined in terms of the data matrix X. EY i β ist im Verallgemei-nerten Linearen Modell nicht mehr linear in den Komponenten von. H X XTX 1XT and determines the fitted or predicted values since.

The predicted values ybcan then be written as by X b XXT X 1XT y. H X X X 1 X is the hat-matrix. For linear models the trace of the projection matrix is equal to the rank of which is the number of independent parameters of the linear model.