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Asked by Tim Bennett
on 3 Apr 2013

I'm calculaing regression coefficients from three sets of angle data ([1 x 20] each) as predictor variables using the following code:

X = [ones(length(x1),1) x1' x2' x3']; B = X\devY';

However, the coefficients obtained are completely different depending on whether I input the angle data as degrees or radians. Therefore,

1) Why does the change in units result in a large difference in the coefficients based on the same data? 2) The different coefficients mean I need to justify the units I will be using to calculate the coeffcients. Any help here would be appreciated.

Any help would be appreciated.

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Answer by the cyclist
on 3 Apr 2013

Are you able to supply a small dataset that shows the problem you are talking about? As you describe it, a uniform factor (unit change) should certainly not affect the coefficients of your model.

Show 4 older comments

Tim Bennett
on 4 Apr 2013

The coefficients [4 x 2] I've obtained from the angle data in degrees are as follows:

0, -0

0.0022, 0.0024

0.0033, -0.0012

0.0028, -0.0014

The coefficients [4 x 2] I've obtained from the angle data in radians are as follows:

0, -0

0.1246, 0.1384

0.189, -0.0711

0.1581, -0.0774

the cyclist
on 4 Apr 2013

Your coefficients simply differ from each other by a factor of 180/pi, the conversion from radians to degrees. This is exactly as expected.

These coefficients presumably have units, just as the inputs do.

Matt Tearle
on 4 Apr 2013

What the cyclist said. If you're solving Xb = y for b and X is in degrees and y is in meters, then b is in meters/degree. Switch X to radians and b will have to change to meters/radian as well.

## 3 Comments

## Walter Roberson (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/69720#comment_140967

This appears to be the same topic as http://www.mathworks.co.uk/matlabcentral/answers/69636-why-does-the-same-angle-data-give-considerably-different-regression-coefficients-depending-on-whethe

## Image Analyst (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/69720#comment_140998

Do you also change the units of devY when you change the units of X?

## Tim Bennett (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/69720#comment_141131

Hi Walter,

the units of devY remain the same. The X predictor variables are joint angles and the Y output variables are related to the position of the foot in meters. I've will attach the code and data i'm using below.