error with curve plotting (polynomial

Hello, i have a data , i imported the data to matlab and draw the plot and from the basic fitting tool i found the polynomial function, however if i coded the polynomiual function it doesnt give me the same graph and i dont know how tol solve this.

I used a cubic function because whenever i use a polynomila degree it tells me it is badly conditioned below is the code i used, i extracted the coef from the basic fitting tool and imge code represents the curve i got from the code

d = @(g)77890-36.98*g+0.007535*g.^2+(1.836*10^(-6))*g.^3-0.06888*g.^4+0.0003544*g.^5;

e = 0:1:2200;

plot(e,d(e));

[ali abbas]

here is my data

Answer 1

[Mathieu NOE]

hello

maybe try this code

clc
clearvars

%  data
data = readmatrix('DATA.xlsx');
x = data(:,1);
y = data(:,2);

% Fit a polynomial p of degree "degree" to the (x,y) data:
degree = 3;
p = polyfit(x,y,degree);

% Evaluate the fitted polynomial p and plot:
f = polyval(p,x);
eqn = poly_equation(flip(p)); % polynomial equation (string)
Rsquared = my_Rsquared_coeff(y,f); % correlation coefficient

figure(3);plot(x,y,'*',x,f,'-')
legend('data',eqn)
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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function eqn = poly_equation(a_hat)
eqn = " y = "+a_hat(1);
for i = 2:(length(a_hat))
    if sign(a_hat(i))>0
        str = " + ";
    else
        str = " ";
    end
    if i == 2
        eqn = eqn+str+a_hat(i)+"*x";
    else
        eqn = eqn+str+a_hat(i)+"*x^"+(i-1)+" ";
    end
end
eqn = eqn+" ";
end
        

Answer 2

[Kumar Pallav]

Hello,

As per my understanding, you expect the same plot using the coefficients extracted from the fitting tool.

I have tried the following code with cubic polynomial:

d = @(g)77890-36.98*g+0.007535*g.^2+(1.836*10^(-6))*g.^3;
e = 0:1:2200;
plot(e,d(e));

and I got the following ouput:

Hope this helps!