finding mathematical function of set of points and draw it

Hello, I have a set of points : x= [10,5 17,5 24,5 31,5] and Y =[5,11804923375421 3,92022009244337 2,14345898571206 1,24047882220866]

The x vector represent the doppler spread values and the Y vector represents the coherence time values, I want to demonstrate that they have an inversely relationship which means Y= a /x . I want to find the value of a and then draw the line

Answer 1

[Andrei Bobrov]

x= [10.5 17.5 24.5 31.5];
Y =[5.11804923375421 3.92022009244337 2.14345898571206 1.24047882220866];

f = fit(x(:),Y(:),fittype('a*x+b'),'StartPoint',[1,1]);
plot(x,Y,'or',xx,f(xx),'-b'),grid on

[yusra Ch]

I want it to be fitted to Y= a/x not Y = a*x+b is it possible ?

[Andrei Bobrov]

f = fit(x(:),Y(:),fittype('a/x'),'StartPoint',1);
plot(x,Y,'or',xx,f(xx),'-b'),grid on

[yusra Ch]

thank you so much Andrei

[Andrei Bobrov]

Maybe you accept this answer, if not, why?

[John D'Errico]

I am debating if I should accept your answer, since I have the privilege.

plot(x,Y,'o')

The two possible fits I might consider here are a linear model as you used, or a cubic. Since there are only 4 points, the cubic will be an exact interpolant.

Honestly, with 4 points that seems nearly linear, a straight line is all that is justified.

But if you know the data is highly accurate, and these deviations are not noise, then a cubic might be far more correct, or some nonlinear sigmoidal model.

The point is, only the person who provided the data knows which is the case. Had you suggested both alternatives and shown the difference, I'd have accepted your answer myself.

Really more data is necessary to guess how to model this process.

[Andrei Bobrov]

Hi John! I'm agree with you.

[yusra Ch]

How can I get the value of a after drawing the fit ?