# Hat Matrix Properties

### Hat Matrix and Leverages Basic idea.

Hat matrix properties. Without simply asserting that the trace of a projection matrix always equals its rank. The hat matrix H is defined in terms of the data matrix X. Up to 10 cash back The hat matrix is a matrix used in regression analysis and analysis of variance.

Where H XXT X 1XT is an n nmatrix which puts the hat on y and is therefore. Computa- tion of a bias-corrected estimator based on the full hat matrix H was problematic due to the near singularity of the matrix I - H. These estimates will be approximately normal in general.

These estimates are normal if Y is normal. We call this the hat matrix because is turns Ys into Ys. New and sharper lower bound for oﬀ-diagonal elements of the Hat matrix in theintercept model which is shorter than those for the no-intercept model.

H X XTX 1XT and determines the fitted or predicted values since. Recall that H hijnij1andhii XiXTX 1XTi. HHH Important idempotent matrix property For a symmetric and idempotent matrixA rankA traceAthe number of non-zero eigenvalues of A.

Frank Wood fwoodstatcolumbiaedu Linear Regression Models Lecture 11 Slide 22 Residuals The residuals like the fitted values of hatY_i can be expressed as linear. Hat Matrix Properties The hat matrix is symmetric The hat matrix is idempotent ie. The hat matrix is idempotent ie.

Use the hat matrix to identify outliers inX. Let 1 be the first column vector of the design matrix X. Estimated Covariance Matrix of b This matrix b is a linear combination of the elements of Y.