fit a curve and equation

Hello,

I have 2 points (x1,y1) and (x2,y2) and wanna fit the power curve with the following shape: sigma=a.x^b+c

and also I know that the b= - 0.5

after fitting I wanna know the value of a and c.

I'll be appreciated if you could help.

best

Answer 1

[Star Strider]

Since you know ‘b’, your system is linear.

This works:

x = [x1 x2];
y = [y1 y2];

B = [x(:).^(-0.5) ones(2,1)] \ y(:);
a = B(1)
c = B(2)

You could also use polyfit.

[Alex]

this is true for linear function, but our system is not linear.

b=-0.5 and we can rewrite the equation like: y=a/sqrtx +c

and we have two points as mentioned. (x1,y1), (x2,y2)

[Star Strider]

Your model is linear. the partial derivative of your objective function with respect to each parameter is not a function of that parameter or any other parameter. That is the definition of ‘linear’ in this context, in that your model is linear in the parameters.

Example —

x = rand(2,1)
y = rand(2,1)

Bnonlin = fminsearch(@(b) norm(y - (b(1)./sqrt(x) + b(2))), [1; 1])
Blin = [x(:).^(-0.5) ones(2,1)] \ y(:)

The estimated parameters from both are essentially the same, allowing for the iteratrive estimation used in fminsearch.

It would not be linear if you were also estimating ‘b’. However you could not uniquely estimate three parameters from two data points regardless of the method you chose.