Two dimensional Linear Regression Hat Matrix
0
$begingroup$
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maarimaari
1
$endgroup$
add a comment |
0
$begingroup$
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maarimaari
1
$endgroup$
$begingroup$
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
$endgroup$
– postmortes
Dec 9 '18 at 19:56
add a comment |
0
0
0
$begingroup$
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maarimaari
1
$endgroup$
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maarimaari
1
asked Dec 9 '18 at 19:54
maarimaari
1
asked Dec 9 '18 at 19:54
maarimaari
1
asked Dec 9 '18 at 19:54
maarimaari
1
asked Dec 9 '18 at 19:54
maarimaari
1
1
$begingroup$
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
$endgroup$
– postmortes
Dec 9 '18 at 19:56
add a comment |
$begingroup$
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
$endgroup$
– postmortes
Dec 9 '18 at 19:56
$begingroup$
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
$endgroup$
– postmortes
Dec 9 '18 at 19:56
$begingroup$
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
$endgroup$
– postmortes
Dec 9 '18 at 19:56
add a comment |
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$begingroup$
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
$endgroup$
– postmortes
Dec 9 '18 at 19:56