Degrees or Radians for angle data?

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.

[Walter Roberson]

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]

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

[Tim Bennett]

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.

Answer 1

[the cyclist]

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.

[Tim Bennett]

First, the code i'm using to obtain the coefficients is as follows:

% X Predictor variables

[M,N] = size(data);

mn = mean(data,2);

dev = data-repmat(mn,1,N);

x1 = dev (1,:);

x2 = dev (2,:);

x3 = dev (3,:);

% Y output variables

mnY = mean(Y,2);

devY = Y-repmat(mnY,1,N);

%Coefficients

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

B = X\devY'

[Tim Bennett]

Data from Predictor Variables (PV) in degrees, where each PV is a [1 x 10] vector:

PV1: 47.2537, 44.6884, 45.8583, 48.2145, 46.0579, 48.5949, 42.096, 46.0047, 46.1201, 44.4573.

PV2: -64.8887, -67.3449, -68.645, -63.1422, -59.4189, -61.6394, -59.9642, -62.5776, -60.138, -63.1737.

PV3: 38.2869, 34.2405, 31.7914, 34.2997, 32.6586, 32.9091, 34.0009, 38.4582, 35.3904, 31.3359.

[Tim Bennett]

Data from Predictor Variables (PV) in radians, where each PV is a [1 x 10] vector:

PV1: 0.8269, 0.782, 0.8025, 0.8438, 0.806, 0.8504, 0.7367, 0.8051, 0.8071, 0.778.

PV2: -1.1356, -1.1785, -1.2013, -1.105, -1.0398, -1.0787, -1.0494, -1.0951, -1.0524, -1.1055.

PV3: 0.67, 0.5992, 0.5564, 0.6002, 0.5715, 0.5759, 0.595, 0.673, 0.6193, 0.5484.

[Tim Bennett]

Data from output variables (OV) in meters (same for both sets of angle data in different units), where each OV is a [1 x10] vector:

OV1: 0.2897, 0.298, 0.2534, 0.3007, 0.3149, 0.2797, 0.2858, 0.2789, 0.3095, 0.2438.

OV2: -0.6777, -0.667, -0.6481, -0.6729, -0.6741, -0.6449, -0.6804, -0.6513, -0.6697, -0.6617.

[Tim Bennett]

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]

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]

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.