How to create a curve fit for my data?

I have the following function: . How can I create a curve fit for my data points?

Answer 1

[Star Strider]

Assuming you have a vector of ‘T’ values that are functions of ‘s’, ‘g’ is given and the parameter to be estimated is ‘x’:

Tfcn = @(x,s,g) 2*pi*sqrt((x+s.^2)./(g.*s));                % Objective Function

s = 1:20;                                                   % Create Data
T = rand(size(s))*10;                                       % Create Data

g = 9.81;
X0 = 1;
X = fminsearch(@(x) norm(T - Tfcn(x,s,g)), X0);             % Estimate Parameters

figure
plot(s, T, '.')
hold on
plot(s, Tfcn(X,s,g), '-r')
hold off
grid

.

[Arpad Takacs]

Thank you so much! And how can I calculate the error of the coefficient 'x'? My data also have an error which should be counted as well.

[Star Strider]

As always, my pleasure!

If you have the Statistics and Machine Learning Toolbox, use the fitnlm function (introduced in R2013b). It will provide confidence limits on the parameters automatically, and the ‘Tfcn’ will work with it, with one small change in the calling syntax:

mdl - fitnlm(s, T, @(x,s)Tfcn(x,s,g), X0)

Then see the fitnlm documentation I linked to to understand how to get even more information from the ‘mdl’ variable and associated functions.

The nlinfit function is also an option (with the same calling syntax as for fitnlm) for ‘Tfcn’. See that documentation and related functions such as nlparci and nlpredci (linked to in that documentation).