# Polyfit returns the wrong correlation coeffcient when I try do a linear regression

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A LL on 11 Nov 2020
Edited: A LL on 14 Nov 2020
Hello :)
I am trying to do a linear regression for a set of data, but the regression coefficient returned by matlab polyfit don't fit my data.
The data is plot just fine but the linear regression function seems very odd...
Please see the attached figure
I tried to plot with polyval (option 1) and with a linear relation (y=ax+b) (option 2) but it does not make any difference... The regression coefficient returned are just no the good ones...
Can anyone help me?
subwFMA = w10MeanFMA(521:771, 41:161); %sub mean wind speed
subssrdFMA = ssrdMeanFMA(521:771, 41:161); %sub mean solar radiation
%OPTION 1
pFMA = polyfit(subwFMA(:),subssrdFMA(:),1); %find regression coefficient a and b for a linear regression
fFMA = polyval(pFMA,subwFMA(:)); %linear regression function
figure(1)
plot(subwFMA(:),subssrdFMA(:),'o',subwFMA(:),fFMA,'-');
%OPTION 2
polyfitFMA = polyfit(subwFMA(:),subssrdFMA(:),1); %find correletation coefficient a and b for a linear regression
aFMA = polyfitFMA(1,1); %coeff a
bFMA = polyfitFMA(1,2); %coeff b
yssrdFMA = aFMA*subwFMA(:) + bFMA; %linear regression function
figure(2)
plot(subwFMA(:),subssrdFMA(:),'o',subwFMA(:),yssrdFMA,'-');
I also tried to reverse my x and y data in polyfit but it makes things even worse!
Thanks
##### 3 CommentsShow 1 older commentHide 1 older comment
A LL on 12 Nov 2020
Hi John,
I am sorry for the confucion, what I mean to do is to do a linear regression with my data by computing the regression coefficient (I think this is the correct expression).
When I plot the linear regression obtained from the polyfit function it does not seem to properly fit my data and I do not understand why this is happening because the data are correctly plot on my figure.
Thanks
John D'Errico on 12 Nov 2020
Again, we don't have your data. And it seems like you fit only a small portion of the data. So how can we possibly know what you did wrong?

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### Accepted Answer

Jon on 11 Nov 2020
Edited: Jon on 11 Nov 2020
I don't think you are plotting your fitted y values
For example where you have
fFMA = polyval(pFMA,subwFMA(:)); %linear regression function
figure(1)
plot(subwFMA(:),subssrdFMA(:),'o',subwFMA(:),yssrdFMA,'-');
I think you want
yssrdfFMA = polyval(pFMA,subwFMA(:)); %linear regression function
figure(1)
plot(subwFMA(:),subssrdFMA(:),'o',subwFMA(:),yssrdFMA,'-');
and where you have
figure(2)
plot(subwFMA(:),subssrdFMA(:),'o',subwFMA(:),fFMA,'-');
I think you want
figure(2)
plot(subwFMA(:),subssrdFMA(:),'o',subwFMA(:),yssrdFMA,'-');
##### 5 CommentsShow 3 older commentsHide 3 older comments
Jon on 13 Nov 2020
Edited: Jon on 13 Nov 2020
I agree, I would expect your fit line to go more through the cloud even if there were very little correlation. So I think you also have a programming error.
You said you made some edits to your code since the original one you posted. Can you please provide your current code (please use the code button on the MATLAB answers toolbar to get it nicely formatted). Also if you can provide your input file, as John D'Errico suggested that would be even better.
A LL on 13 Nov 2020
Edited: A LL on 14 Nov 2020
Ok, thanks again for your help!
I will go over my code one more time and if I can not find the error I will post it here. :)
update: I was able to solve my problem. I had a mistake in my code. Thanks again for your help!

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