Curve Fitting Tool - Power Fit

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)

Answer 1

[Mathieu NOE]

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


        

[Mathieu NOE]

hello again

problem solved ?

[Mathieu NOE]

hello

do you mind accepting my answer ?

tx

[Mohamed Rashad]

Yeah. Forgive me Mathieu. I was kind of busy in studies. Thank you for your answer.

[Mathieu NOE]

No problem

my pleasure ! and have a good day