# How to get polynomial equation of polyfit?

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Berk Cem Yamanlar on 14 Dec 2021
Commented: Steven Lord on 14 Dec 2021
Hello. I have the following code and the data. I need to find the equation of the polynomial and write it on the graph. Also, I will be changing the x and y datas so, it needs to be specific for a set of datas. Thank you for your help! It will be appreciated!!
clc;
clear;
y = [4.0432,4.1073,4.0899,4.1319,4.2885,4.4305,4.5249,4.6172,4.6962,4.7235,4.5987,4.7927,4.895,4.9079];
x = [1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012];
pf = polyfit(x,y,2);%Calculating the corresponding polynomial function
disp('The coefficients of the desired polynomial:');
fprintf('%3.3f\n',pf) %Showing the coefficients of the fitted polynomial function
pv = polyval(pf,x);%Calculating the values of polynomial function at x's
disp('The values of polynomial at given set of x values:');
fprintf('\n %3.3f',pv)
scatter(x,y)
hold on
plot(x,pv)
hold off
##### 2 CommentsShowHide 1 older comment
Berk Cem Yamanlar on 14 Dec 2021
This is the simple linear regression line for my data and there is the equation of the line. I would like to find the equation of second order polynomial and show the equation on the figure as below. Mathieu NOE on 14 Dec 2021
hello
my suggestion below :
the equation is given by the string eqn code :
clc;
clear;
y = [4.0432,4.1073,4.0899,4.1319,4.2885,4.4305,4.5249,4.6172,4.6962,4.7235,4.5987,4.7927,4.895,4.9079];
x = [1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012];
% Fit a polynomial p of degree "degree" to the (x,y) data:
degree = 2;
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,'o',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
Steven Lord on 14 Dec 2021
fprintf lets you automatically include the sign of the variable if you include the flag + in your format specifier. The leading + in the result is a little awkward looking, but the command itself is quite simple and you could post-process the string to trim a leading + and to replace x^1 and x^0 with x and nothing if desired.
coeffs = [3 -4 5];
powers = 2:-1:0;
s = sprintf('%+dx^%d', [coeffs; powers])
s = '+3x^2-4x^1+5x^0'
if s(1) == '+'
s = s(2:end);
end
s = replace(s, 'x^1', 'x');
s = replace(s, 'x^0', '')
s = '3x^2-4x+5'

KSSV on 14 Dec 2021
fprintf('%f*Year^2+%f*YEar+%f\n',pf)
Berk Cem Yamanlar on 14 Dec 2021
Thank you sir! It was very helpful

R2021b

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