How to find the best second degree polynomial to approximate (Linear Algebra)

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Nemanjavuk69

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Mar 23, 2022
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Hello

I am doing a homework and are stuck on this subproblem. I would like some guidance at where to begin. The problem is stated below and the equations are linked and numerated as well.


We look at a simpler problem. "Which second degree polynomial (1) best approximates five given data points", and investigate this using the method of least squares. Set up the 5 X 3 matrix corresponding to the matrix X (2) if the five data points are (3).

(1)
1675197522827.png

(2)
1675197604412.png

(3)
1675197560499.png

Hope to hear from someone and have a great night or day forward!
 
After trying for some time, this is all I can come up with for an [imath]X[/imath]
1675200281660.png

Please do quote this message and give me constructive feedback if something is wrong or not. I also that for some [imath]\hat{u}[/imath] the least squares can be written as [imath]Xu=v[/imath]
 
blamocur said:
Why so many parentheses?
How did you get your matrix X?
What have you learned about quadratic approximations (a.k.a quadratic regressions) ? About polynomial regressions?
Have you searched online about the topic? E.g., https://en.wikipedia.org/wiki/Polynomial_regression.
Click to expand...
Hello

First off, the parenthesis thing is something Maple does, I have no control over the syntax of a programming language.

Second off, the matrix X was given in the homework. If you are referring to my other X which I “tried” to list, all I did was inserting “v” into it.

Third off, I have a very limited knowledge about regression, some my math course does not focus on regression. I know some linear regression but none about quadratic regressions.

Lastly, I have been searching around for the topic but can’t really seem to find head and tails in everything. I will read what you linked and get back to you tomorrow, I will still need to do some research.

Thank you for giving me somewhere to start from. Have a great night/ day forward!
 
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