hello
so basically you permute x and y data and then you get the new result
in my equation output you have to permute x and y names
so that y = 5.0288 + 1.0288*x -0.018926*x^2 becomes x = 5.0288 + 1.0288*y -0.018926*y^2
if you want the code to behave this way , simply change these 3 lines in the function "poly_equation"
eqn = " y = "+a_hat(1);
eqn = eqn+str+a_hat(i)+"*x";
eqn = eqn+str+a_hat(i)+"*x^"+(i-1)+" ";
into
eqn = " x = "+a_hat(1);
eqn = eqn+str+a_hat(i)+"*y";
eqn = eqn+str+a_hat(i)+"*y^"+(i-1)+" ";
% what you did
% x = [12;8;7;10;16;15;12;12;20;19;19;17;20;16]; % data
% y=[3.225;4.725;6.225;7.725;9.225;10.725;12.225;13.725;15.225;16.725;18.225;19.725;21.225;22.725]; % depth
% what you want
y = [12;8;7;10;16;15;12;12;20;19;19;17;20;16];
x=[3.225;4.725;6.225;7.725;9.225;10.725;12.225;13.725;15.225;16.725;18.225;19.725;21.225;22.725];
% 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(1);plot(x,y,'*',x,f,'-')
legend('data',eqn)
title(['Data fit , R² = ' 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+" + "+a_hat(i)+"*x";
eqn = eqn+str+a_hat(i)+"*x";
else
% eqn = eqn+" + "+a_hat(i)+"*x^"+(i-1)+" ";
eqn = eqn+str+a_hat(i)+"*x^"+(i-1)+" ";
end
end
eqn = eqn+" ";
end
