Curve Fitting Tool - Power Fit

Question

Mohamed Rashad 2021-10-13

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1562586-curve-fitting-tool-power-fit

评论： Mathieu NOE 2021-12-8

2021-10-13.png

So I have been trying to match the Power fit Curve obtained from my Program and the one Obtained using curve fitting tool. In the curve fitting tool i get a result saying "Cannot fit Power functions to data where X has nonpositive values". So here is my code and I have attached the screenshots of both Plots. Suggest me how to make this right. Thank You.

clc

clear;

x=[0.75; 2; 3; 4; 6; 8; 8.5];

y=[1.2; 1.95; 2; 2.4; 2.4; 2.7; 2.6];

fit(x,y,'power1')

ans =

General model Power1: ans(x) = a*x^b Coefficients (with 95% confidence bounds): a = 1.491 (1.239, 1.743) b = 0.2802 (0.1807, 0.3797)

a = 1.491;

b = 0.2802;

X=0:0.1:9;

Y=(a.*(X.^b));

plot(X,Y)

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Answer 1

Mathieu NOE 2021-10-13

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1562586-curve-fitting-tool-power-fit#answer_807701

在 MATLAB Online 中打开

hello

even without the curve fitting toolbox you can get a good match using fminsearch :

sol = 1.4912 0.2802

clc
clearvars
% data
x=[0.75; 2; 3; 4; 6; 8; 8.5];
y=[1.2; 1.95; 2; 2.4; 2.4; 2.7; 2.6];
%power fit 
f = @(a,b,x) a.*x.^b;
obj_fun = @(params) norm(f(params(1), params(2),x)-y);
sol = fminsearch(obj_fun, [1,1]);
a_sol = sol(1);
b_sol = sol(2);
x_fit = linspace(0,10,300);
y_fit = f(a_sol, b_sol, x_fit);
    
Rsquared = my_Rsquared_coeff(y,f(a_sol, b_sol, x)); % correlation coefficient
figure(3);plot(x,y,'o',x_fit,y_fit,'-')
title(['Data fit - R squared = ' num2str(Rsquared)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Rsquared = my_Rsquared_coeff(data,data_fit)
    % R2 correlation coefficient computation
    
    % The total sum of squares
    sum_of_squares = sum((data-mean(data)).^2);
    
    % The sum of squares of residuals, also called the residual sum of squares:
    sum_of_squares_of_residuals = sum((data-data_fit).^2);
    
    % definition of the coefficient of correlation is
    Rsquared = 1 - sum_of_squares_of_residuals/sum_of_squares;
    
    
end
        