MATLAB: Calculating linear fit with respect from origin (0,0)

linearpolyfitpolyval

I have a data of DataX and Data Y, which is plotted in the blue line as in picture.I am trying to analyse how much the blue line is deviated from the black dotted line x and y = [0:1:7]. The thing is, if i want to compare the linear fit, the linear fit of my data does not start from 0 (yellow line).
Can anyone suggest what kind of metric that I can use here? If possible, I would like a way to measure say for example if the fit of my data falls below the dotted line, the value will be <0, and if it is above the >0.

Best Answer

Ok, you just have to use the right statistics. Look here:
%random points
x=1:10;
y=rand(1,10);
%fit data
p=polyfit(x,y,1);
yfit=p(2)+x*p(1);
%residuals
yres = y-yfit;
%deviation from mean
ymean = mean(y(:));
ydev = y-ymean;
%compute R2
SSR = sum(yres.^2);
SST = sum(ydev.^2);
R2 = 1-SSR/SST;
%plot fitting
plot(x,y,'b',x,yfit,'r');
The R2 number is Rsquared statistics explaining how the fit line well represents the points.
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