How can we fit hyperbola to data?

Hi, I have x and y coordinates for my data points. The data is fitted well with exponential fitting. However, I have to fit a hyperbola (a must condition for my results). I am using code,

% fit data k=0.002; % hit and trial

x = 1/xdata; y = k*1/x; p=plot(x,y)

I have attached excel file of my data. Accept my thanks in advance.

Answer 1

[Star Strider]

Try this:

D = xlsread('data for hyperbola fitting.csv');
D = sortrows(D,1);
x = D(:,1);
y = D(:,2);

hyprb = @(b,x) b(1) + b(2)./(x + b(3));                 % Generalised Hyperbola

NRCF = @(b) norm(y - hyprb(b,x));                       % Residual Norm Cost Function
B0 = [1; 1; 1];
B = fminsearch(NRCF, B0);                               % Estimate Parameters

figure(1)
plot(x, y, 'pg')
hold on
plot(x, hyprb(B,x), '-r')
hold off
grid
text(0.7, 0.52, sprintf('y = %.4f %+.4f/(x %+.4f)', B))

‘Accept my thanks in advance.’

The sincerest expression of appreciation here on MATLAB Answers is to Accept the Answer that most closely solves your problem.

[ishita agrawal]

Thank you so much.

[Star Strider]

As always, my pleasure!

[lakshmikanth ayyadevara]

code is really nice

[Rik]

@lakshmikanth ayyadevara Flags are not personal bookmarks, they are to alert staff and members with editing privileges. I have removed your flag.

[Raj Lakhani]

@Star Strider can you also show how to evaluate the R(square) after this? thanks in advance

[Rik]

Have you read the Wikipedia article about the R2? It is actually fairly easy to write code that calculates it.

[Star Strider]

@Raj Lakhani —

D = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/87569/data%20for%20hyperbola%20fitting.csv');
D = sortrows(D,1);
x = D(:,1);
y = D(:,2);

hyprb = @(b,x) b(1) + b(2)./(x + b(3));                 % Generalised Hyperbola

B0 = [1; 1; 1];
mdl = fitnlm(x, y, hyprb, B0)

mdl = 
Nonlinear regression model:
    y ~ b1 + b2/(x + b3)

Estimated Coefficients:
           Estimate        SE        tStat        pValue  
          __________    ________    ________    __________

    b1      0.094879    0.015709      6.0399    2.4472e-09
    b2       0.14875    0.017335      8.5807    5.5591e-17
    b3    -0.0097497    0.029435    -0.33123       0.74057


Number of observations: 739, Error degrees of freedom: 736
Root Mean Squared Error: 0.0502
R-Squared: 0.772,  Adjusted R-Squared 0.772
F-statistic vs. constant model: 1.25e+03, p-value = 2.94e-237

B = mdl.Coefficients.Estimate;

figure(1)
plot(x, y, 'pg')
hold on
plot(x, hyprb(B,x), '-r')
hold off
grid
xlabel('x')
ylabel('y')
text(0.7, 0.52, sprintf('$y = %.4f + \\frac{%.4f}{x %+.4f}$', B), 'Interpreter','latex', 'FontSize',12)

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