Fitting a curve to data

Hello,

I am trying to test out the validity of Taylor-Sedov analytical solution to an experimental data set.

I want to fit curves of the form

y=At^2

y=At^3

to some data points, where A is malleable and will be changed to achieve the best fit.

Advice is greatly appreciated.

Answer 1

[the cyclist]

If you have the Statistics Toolbox, you can use the nlinfit() function. Here is an example of doing the fit with Ax^2. It should be obvious how to adapt it for Ax^3.

% Here is an example of using nlinfit(). For simplicity, none of
% of the fitted parameters are actually nonlinear!

% Define the data to be fit
x=(0:1:10)'; % Explanatory variable
y = 7*x.^2; % Response variable (if response were perfect)
y = y + 15*randn((size(x)));% Add some noise to response variable

% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(A,x) A.*x.^2;
A_fitted = nlinfit(x,y,f,[1]);

% Display fitted coefficients
disp(['A = ',num2str(A_fitted)])

% Plot the data and fit
figure(1)
plot(x,y,'*',x,f(A_fitted,x),'g');
legend('data','fit')