How to find the best fit curve as a vertical scaling of another curve?

I have a original graph of function f(x). Now I have few points scattered and I want to find a best fit curve through these points. But my new fit curve should be of the form n*f(x) where n is a numerical value. I want to find the value n. How can I do this? Below figure might explain the problem I am talking about. I want to fit curve n*f(x) through orange points and find out n.

Answer 1

[David Goodmanson]

Hi SojM,

Suppose you have points x,y for the function f(x), where x and y are column vectors. And suppose the red points are the set xr,yr, also both column vectors. Then

ynew = interp1(x,y,xr,'spline');
n = ynew\yr

If you have f(x) as an algebraic function, then the first line can be simply

ynew = f(xr) 

[SojM]

Thanks. This is what I was looking for. Is there any way to put this into a for loop when x and y are same but there are multiple column vectors data (xr, yr)?