Determining components of components of a PCA using princomp()

Hi, I'm new to PCA so this might not be the right question. I'm trying to use princomp() to get a better understanding of what's driving my data set, and there are about 10 components that end up driving 99% of the variability. (It's a big data set, and I'm measuring growth over time periods specifically, hopefully to make the statistical analysis more rigorous)

However, I can't figure out what the output components translate to in my original data set, i.e. which combinations of variables they correspond to. Can someone help me figure out what these components are, or alternatively tell me what I'm getting wrong about PCA?

Thanks!

Answer 1

[the cyclist]

The description of the outputs is here: http://www.mathworks.com/help/toolbox/stats/princomp.html.

The first output, called "COEFF" in the documentation, is the matrix of coefficients of the principal components. Each column of COEFF identifies the linear combination of one of the principal components. So, for example, if the first column of COEFF is

>> [0.6435; 0.0102; 0.2754; ....]

then the first principal component is

P1 = 0.6435*x(:,1) + 0.0102*x(:,2) + 0.2754*x(:,3) + ...

etc.

Does that help?