MATH 423 Lecture Notes - Lecture 21: Covariance
19 Nov 2018
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Hy. is the hat matrix or the influence matrix. Thus hij isthe at whichthe ith fitted value changes as we vary the in observation the influence thatobservation has on that. Ted value f oiin z symmetry r sirlh. is. Asymmetric idempotent matrix is a projection matrix this means that h projects y into a lower dimensionalsubspace i hy is a linearcombination. Specifically y is a point in rn but of no vectors namely the two columns of x in otherwords. H projects y onto the column space ofx. The column space of x is the setof vectors that can bewritten as linear combinations of x. The vector of residuals is eiy y y hy. Hereare some propertiesof eh i influence i hj li hitei h z symmetry. Y y hy eh eh lehllxfteecji. Eili hixftli hiej xp xxixixtxfoer r i cancel. eu. Thusthe variance of each residual is notquite g nor are the residuals exactly uncorrelated htt. Lie i h c.
