Problem interpreting regression coefficient output

I'm try and compute regression coeffients between mean free joint angles (ankle, hip, knee angles time-normalised to 101 data points) as predictor variables (X = x1, x2, x3) and changes in the mean-free foot COM as an outcome variable (y)

I've just entered the following into Matlab:

X = [ones(size(x1)x1 x2 x3];

B = X\y

where the dimensions of y, x1, x2, and x3 are 1 x 20 each. However the B output is giving me a 80 x 20 matrix filled with zeros apart from row 44 that contains a range of values (e.g 0.0006 0.0033 -0.002 etc). Are these the coeffiecents as I was expecting a single vector column of coefficients?

Any help would be appreciated.

Answer 1

[Star Strider]

You need to transpose x1, x2, and x3 to be [20 x 1] to form your X matrix:

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

and if y is not also already a column vector, it needs to be. Assuming y is currently a row vector as well, your multiple linear regression parameter estimation statement becomes:

B = X\y';

That should work.

That the B you calculated is an [80 x 20] matrix filled with zeros results from your current X (not the one I constructed here) being an 80-element row vector rather than the [20 x 4] matrix you intended.