Contents
Linear regression
Create a figure with white background
h=figure; set(h,'Color','w') hold all title('Linear regression by the method of least squares') xlabel('x'); ylabel('y,y_m')
Measured values
Here the "measured" values are determined artificially using the function 2x+5 and introducing some randomnes for simulation of the measurement error.
x=0:0.1:1; N=length(x); ym=2*x+5*ones(size(x))+0.1*rand(size(x))-0.05*ones(size(x)); % Plot the measured values using circles plot(x,ym,'ok')
Calculate the ecuation of the best fitting line using the method of
least squares
First the 'hardest way'
sumx=sum(x); sumx2=sum(x.^2); sumym=sum(ym); sumxym=sum(x.*ym); C=[sumx2 sumx; sumx N]; D=[sumxym; sumym]; % The solution of a linear equation system can be calculated in two ways: % First: A=C\D; % Second: A=inv(C)*D; % Now the vector 'A' contains the parameters of the best fitting line. % Calculate the points of the line and plot the line. y=polyval(a,x); plot(x,y,'-k');
Using polyfit
Secondly the easiest way
a=polyfit(x,ym,1); % Now the vector 'a' contains the parameters of the best fitting line. % Calculate the points of the line and plot the line. y=polyval(a,x); plot(x,y,'-r'); legend('measured','estimated-hardest','estimated-easiest')
