Question

I have these four variables:

Class1 
Class2
Class3 
Class4

Each of them is a matrix.

They are inside a matrix X.

X = [[Class1]' [Class2]' [Class3]' [Class4]']

I apply a corrcoef function to X.

B = corrcoef(X)

to obtain the result:

B = 1.0000   -0.2392    0.9533    0.6903
   -0.2392    1.0000   -0.1272    0.4267
    0.9533   -0.1272    1.0000    0.6971
    0.6903    0.4267    0.6971    1.0000

But I don’t know what this means. How can I interpret these values and what do they mean?

I can’t find help in MATLAB’s help documentation.

Answer 1

If you know the definition of a sample correlation coefficient then the answer is simple.

Since B is 4 by 4, I think I can safely assume that Classz is a row vector of observations on some random variable, and that you have 4 such row vectors. Thus X is a N by 4 matrix, with columns corresponding to random variables 1 to 4, and rows corresponding to observations on the random variables.

If you check the documentation in the link provided by Mark Elliot, you’ll note that this implies that X has the correct orientation for applying the corrcoef function.

The output of corrcoef is the sample correlation matrix. It is 4 by 4 since you have 4 random variables (columns of X) to start with. The diagonals of this matrix correspond to each random variables correlation with itself (hence they’re all equal to 1). The off-diagonals correspond to sample correlation coefficients between the random variables. That is, the number in element (2, 3) is the sample correlation coefficient between random variable 2 and 3 (ie column 2 and 3 of X). Since the sample correlation coefficient between 2 and 3 is the same as between 3 and 2, B is thus symmetric by construction.

Hopefully this clears it up. If the problem is that you don’t know what a correlation coefficient is, then SO is probably not the right forum. Maybe do some research of your own and then if you still have a question post it to Math Exchange.