Least squares interpolation in Octave

Question

I did a physics experiment, and got the following data:

R=[2.91 2.19 1.76 1.43 1.20 1.01 0.88 0.77 0.67 0.6 0.52 0.46 0.41 0.37];
t=[35:5:100];
T=t+273.15;

Now I need to do a least squares interpolation for the formula ln R = f(1 / T). I tried several methods from the web, but could get none of them to work.

Answer 1

Apparently, you are using linear lease square interpolation. The problem exists at the code for calculating coefficients.

This operation

A \ y

works when the column size of A matches with the row size of y.

But in your code, horizontal concatenation of ones(n,1) with x in the statement

A = [x ones(n,1)]

is not being allowed because the size of x is 1*14 and that of ones(n,1) is 14*1. Clearly, you are getting a dimensions mismatch error.

Here is a working code:

R=[2.91 2.19 1.76 1.43 1.20 1.01 0.88 0.77 0.67 0.6 0.52 0.46 0.41 0.37];
t=[35:5:100];
T=t+273.15;


function coeff = least_square (x,y)
    n = length(x);
    A = [ones(n,1) x];
    coeff = A \ y;
    plot(x,y,'x');
    hold on
    interv = [min(x) max(x)];
    plot(interv,coeff(1)*interv+coeff(2));
end


least_square(R', T');