MATLAB: Fitting a parabola giving unreasonable answer

Question

Hello,

I'm trying to fit a parabola to 4 data points using the following equation:

y = a.*exp(((-4.*pi.*b.*6.022e23)./(8.314.*1623)).*(((c./2.*(c-x).^2) - (1/3.*(c-x).^3))));

I'm getting an unreasonable result, which looks like this:

I think the equation is correct because I copy and pasted it from a function that employs it to create this graph, which models the same points:

Best Answer

Two things: I changed your independent values (r) to something that is not so small. Second, I made your equation more simple. I tried it with your original values but it didn't work for me. Hopefully this gets you off to a good start.

%Data
r = [0.89;1.12;1.26;1.42];
D = [0.027322404;1.798850575;1.33;0.11];
%Set up the fit
ft = fittype('a*r^2+b*r+c', 'independent', 'r');
opts = fitoptions('Method', 'NonlinearLeastSquares');
opts.Display = 'Off';
opts.StartPoint = [0.2, 0.2, 0.3];
%Conduct the fit
[fitresult, gof] = fit(r, D, ft, opts);
%Evaluate the function for plotting
a = fitresult.a;
b = fitresult.b;
c = fitresult.c;
r_model = linspace(min(r), max(r), 100); %create 100 points to evaluate the model on
D_model = a*r_model.^2+b*r_model+c;
%Make plots
plot(r, D, 'bo', 'markerSize', 6) %plot the data
hold on
plot(r_model, D_model, 'LineWidth', 2, 'Color', 'r') %plot the model
leg = legend('Data', 'Model');
leg.FontSize = 14;

Related Solutions

MATLAB: Changing matrices form, echelon the matrices

A=[0  1  0  0
  0  0  1  1
  0  0  0  1
  0  0  0  0]

%For the first case

n=size(A,1)
out=[A(1,:)';cell2mat(arrayfun(@(x) A(x,x+1:n)',(2:n-1)','un',0))]

% Forthe second case

B=A';
B=B(:)

MATLAB: How to specify a model asa FITTYPE object and not as a function using the Curve Fitting Toolbox

You can specify a FITTYPE object as your fit model in FIT function.

Use an object FITTYPE (different from CFIT). Here is an example which demsonstrates how to do this:

   f1 = fittype('a*x+b')
 f1 =
      General model:
        f1(a,b,x) = a*x+b

Now, you can use this model to fit different data set. For example:

x = 0:10; y = sin(x);
f2 = fit(x',y',f1)
 f2 =
   General model:
     f2(x) = a*x+b
   Coefficients (with 95% confidence bounds):
     a =    -0.02444  (-0.1812, 0.1323)
     b =      0.2505  (-0.677, 1.178)

Related Question

• How to reduce the rmse for a fit obtained using curve fitting toolbox

Answer 1

Two things: I changed your independent values (r) to something that is not so small. Second, I made your equation more simple. I tried it with your original values but it didn't work for me. Hopefully this gets you off to a good start.

%Data
r = [0.89;1.12;1.26;1.42];
D = [0.027322404;1.798850575;1.33;0.11];
%Set up the fit
ft = fittype('a*r^2+b*r+c', 'independent', 'r');
opts = fitoptions('Method', 'NonlinearLeastSquares');
opts.Display = 'Off';
opts.StartPoint = [0.2, 0.2, 0.3];
%Conduct the fit
[fitresult, gof] = fit(r, D, ft, opts);
%Evaluate the function for plotting
a = fitresult.a;
b = fitresult.b;
c = fitresult.c;
r_model = linspace(min(r), max(r), 100); %create 100 points to evaluate the model on
D_model = a*r_model.^2+b*r_model+c;
%Make plots
plot(r, D, 'bo', 'markerSize', 6) %plot the data
hold on
plot(r_model, D_model, 'LineWidth', 2, 'Color', 'r') %plot the model
leg = legend('Data', 'Model');
leg.FontSize = 14;