Content deleted Content added
GreenC bot (talk | contribs) Rescued 1 archive link. Wayback Medic 2.5 |
Bluelink 1 book for verifiability (prndis)) #IABot (v2.0.1) (GreenC bot |
||
Line 75:
Suppose the design matrix <math>X</math> can be decomposed by columns as <math>X= [A~~~B]</math>.
Define the hat or projection operator as <math>P\{X\} = X \left(X^\mathsf{T} X \right)^{-1} X^\mathsf{T}</math>. Similarly, define the residual operator as <math>M\{X\} = I - P\{X\}</math>.
Then the projection matrix can be decomposed as follows:<ref>{{cite book|last1=Rao|first1=C. Radhakrishna|last2=Toutenburg|first2=Helge|author3=Shalabh|first4=Christian|last4=Heumann|title=Linear Models and Generalizations|url=https://archive.org/details/linearmodelsgene00raop|url-access=limited|year=2008|publisher=Springer|___location=Berlin|isbn=978-3-540-74226-5|pages=[https://archive.org/details/linearmodelsgene00raop/page/n335 323]|edition=3rd}}</ref>
:<math>
P\{X\} = P\{A\} + P\{M\{A\} B\},
| |||