Estimate error using MATLAB (least squares)

Question

I have the equation ln(c)=-1/2k^2 * z^2, where y = ln(c), x = z^2 and a = -1/2k^2.

I want to estimate the a, so:

a = polyfit(z.^2, log(abs(c)), 1)

Because I have the (initial) equation c = exp(-z^2/2k^2), from above I am founding two values for a and now I want to estimate k (k1), so I do:

k1 = sqrt(-1/2*a(1))

Now, I want to predict c and error using values of k1 and z. So, I do:

c_predict = polyval(a,z)
c1 = exp((-z.^2)/2*k1^2)
error = c_predict - c1

Or just:

c1 = exp((-z.^2)./2*s1^2)
error1 = c - c1

What is right?

error = c_predict - c1

or

error = c - c1

?

Answer 1

Try looking into the norm command:

relative least squares error = norm(y-y',2)/norm(y)

y is your original signal and y' is the signal your measuring the error of.

See here