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# How to estimate weights of the weighted mean?

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Anudeep on 25 Nov 2020
Edited: Jason Nicholson on 29 Dec 2020
I have an equation of y = (a1x1 + a2x2 + ... + a81x81)/81
I have a set of y and x values to estimate the coefficients a1, a2, ... , a81.
How do I code to derive the coefficients?
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KSSV on 25 Nov 2020
Read about regression, '\', linear least squares.

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### Answers (1)

Jason Nicholson on 29 Dec 2020
Edited: Jason Nicholson on 29 Dec 2020
Put all the each x and y pair on a row. Formulate the matrix A containing all the x1...x81 and x values. Put the y values in a column matrix. Use backslash to linear least squares solve.
pseudo code:
assume each column of x is x1, x2, etc and each row is a point.
A = [x(:,1) x(:,2) ... x(:,81)] in other words, A = x
a = A\y
Note, there is a lot of issues related to stability of this problem. Research linear least squares problem. This is a good place to start: Systems of Linear Equations
Please, remember to accept my answer if it answers your question.
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