1
$\begingroup$

I am studying linear regression. I have studied this in the past, but this is my first time exposing myself to the matrix form of multiple linear regression. My matrix algebra/linear algebra skills are a little rusty and I have been trying to review/relearn a lot of the material so I can better understand the multiple linear regression proofs.

One thing that keeps coming up is quadratic form of random vectors. I am working through some regression proofs using the quadratic form, but I am not sure I fully understand its purpose?

If anyone can explain why they are used, or their purpose either generally or with respect to regression I would be extremely thankful!

$\endgroup$

closed as unclear what you're asking by Xi'an, Yves, user158565, Taylor, Ben Mar 8 at 0:14

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 5
    $\begingroup$ Succinct notations make mathematical statements much easier to read and understand. I can't imagine what we would instead have without the "quadratic forms" you mentioned, maybe tons of summations and dot dot dots? May I suggest that you embrace these notations with a leap of faith then re-evaluate their usefulness after you are familiar with them? $\endgroup$ – Ye Tian Mar 4 at 5:16
1
$\begingroup$

Quadratic forms are everywhere in mathematics, so by recognizing them in regression (or elsewhere) you will find that the necessary work is probably already done. Regression (and ANOVA) is built on sums of squares, SSR, SSE, SST, ... and those are quadratic forms! By recognizing that you will see a common pattern, and so learn faster.

See this long list: https://stats.stackexchange.com/search?q=sum+of+squares+regression+answers%3A1

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.