Least Squares Regression, Help me find the error in my code!

Suppose the curve you're fitting can follow the form

y = an*x^n+ an-1*x^(n-1)+...+ a1x + a0

x and y are two column vectors of the same size and n is the degree of the polynomial. A is an array of the coefficients, in the order from an to a0.

Solve for A, and the e, the array of the residuals.

Here's what I have: function [A,e] = MyPolyRegressor(x, y, n)

for i= 1:n

    x(i)=x.^(n-1);

end;

A=x/y;

e=A*x-y;

Whenever I run it, it says, "In an assignment A(I) = B, the number of elements in B and I must be the same." Please help!

[Azzi Abdelmalek]

can you post your data?

Answer 1

[Matt J]

In

 x(i)=x.^(n-1);

the left hand side is a scalar location and the right hand side is not a scalar. So there's no room for it. I don't really understand why you're trying to overwrite x with powers of itself like x.^(n-1).

You should consider the VANDER command. I'm assuming you're not allowed to use POLYFIT.

[Matt J]

There is also

 xpowers=bsfun(@power,x(:),0:n);

[SB]

I'd try that, but I'm trying to avoid using any commands beyond basic array ones. I was thinking something like

for i = 1:n

   b(i) = x(i)^(n-i) ;

end

A=b\y';

e=A*b-y;

I can't quite get the answer though.

[Matt J]

b=ones(length(x),n+1);

for i = 0:n-1

     b(:,i+1) = x(:).^(n-i) ;

end

Answer 2

[Azzi Abdelmalek]

There is a problem in your x array size, it should be a matrix (nxm) where m is the length of y and m is the lenngth of unknown variables

[SB]

I fixed that in my current code (shouldve been b*A rather than A*b), but I'm still getting the wrong answer ( the correct answer and my new code is posted above).