Curve fitting tool fits a wrong equation

I am using Matlab for my physical chemistry lab evaluation. Currently I am trying to fit an equation , using the custom equation function. When I fit it works fine, but as soon as I add a second parameter, the fit bocomes linear and I can't figure out why.

[the cyclist]

Can you upload the data? You can use the paper clip icon in the INSERT section of the toolbar.

[Elizaveta Iavorskaia]

I used the following data:

p = [101500, 77300, 61600, 51300, 45000, 39000];

V = [0.03, 0.04, 0.05, 0.06, 0.07, 0.08];

P as x, V as y.

These are the data I collected from the experiment.

[the cyclist]

Also, I don't think this should matter, but just to be absolutely certain, I would try coding the equation as

(a./x) + b

Answer 1

[the cyclist]

I can't figure out what is going wrong here, and I don't have the Curve Fitting Toolbox to play around.

I get a sensible fit using fitnlm, so if you have the Statistics and Machine Learning Toolbox, you could use that if you don't figure this out.

% The data
p = [101500, 77300, 61600, 51300, 45000, 39000]';
V = [0.03, 0.04, 0.05, 0.06, 0.07, 0.08]';

% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x) F(1)./x + F(2);

% Define starting guess of coefficients
beta0 = [1000 1];

% Fit the model
mdl = fitnlm(p,V,f,beta0);

% Plot the data and fit
figure
plot(p,V,'*',p,predict(mdl,p),'g');
xlabel("p")
ylabel("V")
legend('data','fit','Location','NorthEast')

[John D'Errico]

The problem is almost certainly a poor choice of starting values when this happens. And since the curve fitting toolbox uses random starting values when none are provided, sometimes it gets it wrong.

[Elizaveta Iavorskaia]

Thank you very much for the answers!

[Matt J]

To get a better starting guess:

StatPoint=polyfit(1./x,y,1);