# Calculating linear fit with respect from origin (0,0)

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Sharah 2016 年 9 月 28 日

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.
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Sharah 2016 年 9 月 28 日
Say, if I have data line the blue line, but it falls above the dotted line. What I want to do is to calculate how much the blue data is different from the dotted line.
The following is one of the method that I used, but not sure if this is accurate
function [rsq] = linearity(xData, yData)
xlin = 0:max(xData)/(length(xData)-1):max(xData);
ylin = 0:max(xData)/(length(xData)-1):max(xData);
p = polyfit(xlin, ylin,1);
yfit = p(1) * xlin +p(2); %similar to polyval(p, x)
yresid = yData - yfit';
SSresid = sum(yresid.^2);
SStotal = (length(yData)-1)*var(yData);
rsq= 1-SSresid/SStotal;
In which I calculated the Rsquare of my data relative to the linear fit of blue line? Will that be correct?

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### 採用された回答

Massimo Zanetti 2016 年 9 月 28 日

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.
##### 2 件のコメント表示非表示 1 件の古いコメント
Massimo Zanetti 2016 年 9 月 28 日
Ok, so it is much simple. Just replace the polyfit line with reference one.
%random points
x=1:10;
y=rand(1,10);
yref=1:10;
%residuals
yres_ref = y-yref;
%deviation from mean
ymean = mean(y(:));
ydev = y-ymean;
%compute R2
SSR = sum(yres_ref.^2);
SST = sum(ydev.^2);
R2 = 1-SSR/SST;
%plot fitting
plot(x,y,'b',x,yref,'r');

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