Trouble fitting a curve using polyfit and polyval

I have to fit a straight line to the mean-variance scatterplots of an image channel. I am expected to use polyfit and polyval functions for these. The fitted lines would have the form: noise variance = a*signal mean+b, and I have to find a and b. I tried matlab documentation, but couldn't understand how to proceed. How can I do this?

Answer 1

[Mathieu NOE]

hello

see example below :

clc
clearvars

%  data
x = (0:100);
b = 1.5;
a = 2.35;
y = a + b*x + 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)
Rsquared1 = my_Rsquared_coeff(y,f); % correlation coefficient

figure(1);plot(x,y,'o',x,f,'-')
legend('data',eqn)
title(['Data fit - R squared = ' num2str(Rsquared1)]);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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