How to estimate weights of the weighted mean?

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?

[KSSV]

Read about regression, '\', linear least squares.

Answer 1

[Jason Nicholson]

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

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