Hat Matrix H

The hat matrix is also known as the projection matrix because it projects the vector of observations y onto the vector of predictions thus putting the hat on y.

Hat matrix h. In hindsight it is geometrically obvious that we should have had H2 H. 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. The predicted values ybcan then be written as by X b XXT X 1XT y.

Along the way I present the proo. H X XTX 1XT and determines the fitted or predicted values since. Where H XXT X 1XT is an n nmatrix which puts the hat on y and is therefore referred to as the hat matrix.

This shows that the. H XX t X-1 X t. Leverage considered large if it is bigger than twice the mean leverage value 2pn.

The relationship between the two is. 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.

How can we prove that from first principles ie. I prove these results. Tukey coined the term hat matrix for Hbecause it puts the hat on y.

The matrix H is called the hat matrix because it maps the vector of observed values into a vector of fitted values. The Delivery Times Data A soft drink bottler is. Sie trägt den Namen Hat-Matrix weil die Schätzwerte eines Regressionsmodells englisch gesprochen.