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

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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 Comments

John D'Errico
on 12 Nov 2020

### 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,'-');

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