How to obtain r^2 (r squared) value of linear regression plotted using 'lsline'

Question

Gucci 2022-3-21

1
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https://ww2.mathworks.cn/matlabcentral/answers/1676854-how-to-obtain-r-2-r-squared-value-of-linear-regression-plotted-using-lsline

回答： Mathieu NOE 2022-3-22

Hello, what is the syntax to obtain the r-squared (r^2) value if I plotted a best fit linear regression with the 'lsline' function?

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Scott MacKenzie 2022-3-21

You can't get r^2 from lsline. lsline is created from the points. To get r^2, you also need to work with the points. Use the corrcoef function to get r (and then r^2) from the points.

Gucci 2022-3-21

Thanks

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Answer 1

Mathieu NOE 2022-3-22

2
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1676854-how-to-obtain-r-2-r-squared-value-of-linear-regression-plotted-using-lsline#answer_923834

在 MATLAB Online 中打开

hello

see suggestion below - even no need of lsline

clc
clearvars
% dummy data
x = (0:100);
a = 1.5;
b = 0.235;
y = a*x +b + 3*randn(size(x));
% Fit a polynomial p of degree "degree" to the (x,y) data:
degree = 1;
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
        