how to make the trend line identifies x as dependant variable

Hello

my code is :

data = [12;8;7;10;16;15;12;12;20;19;19;17;20;16];
depth=[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];
 figure
 plot(data,depth,'or')

 set ( gca, 'Ydir', 'reverse' )
ylabel('D (m)') 
    xlabel('N') 

The resulting quadratic trendline equation is: y=-0.0038x^2+1.21x-3.69 where x relates to N

However, x values (or N) are the dependant variables in reality. In fact, I want the regression (least square method) consider y (or D) values as independant variable. How can I get the correct equation such as x=...y^2+...y-...?

Answer 1

[Mathieu NOE]

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
        

[Mathieu NOE]

Hello

Problem solved ?