# corrms, corrxs¶

## Purpose¶

Computes the observed correlation matrix.

## Format¶

cx = corrms(m)
cx = corrxs(x)
Parameters: m (KxK moment (x'x) matrix) – A constant term MUST have been the first variable when the moment matrix was computed. x (NxK matrix) – data cx (PxP correlation matrix) – For corrms(), $$P = K-1$$. For corrxs(), $$P = K$$.

## Examples¶

// Set rnd seed for reproducible results
rndseed   8989;

// Assign x1 and x2
x1 = rndn(3, 3);
x2 = ones(3, 1)~x1;

print "x1 :" x1;
print "x2 :" x2;


After the above code, x1 and x2 look like:

x1 :
0.010555555     -0.045969063       0.12701699
1.6454828        1.2380373       0.53988699
1.1556776      -0.53575797       0.14056238
x2 :
1.0000000      0.010555555     -0.045969063       0.12701699
1.0000000        1.6454828        1.2380373       0.53988699
1.0000000        1.1556776      -0.53575797       0.14056238


Continuing from above code,

// Correlation of x1 with x1
print "corrxs(x1) :" corrxs(x1) ;

// Correlation of moment = x2'x2
m = x2'x2;
print "corrms(x2'x2) :" corrms(m);


After the above code,

corrxs(x1) :
1.0000000       0.52196856       0.75039768
0.52196856        1.0000000       0.95548228
0.75039768       0.95548228        1.0000000
corrms(x2'x2) :
1.0000000       0.52196856       0.75039768
0.52196856        1.0000000       0.95548228
0.75039768       0.95548228        1.0000000


## Remarks¶

The correlation matrix is the standardized version of the correlation/covariance matrix computed from the input data, that is, it divides the sample size, $$N$$, rather than $$N - 1$$. For an unbiased estimate correlation/covariance matrix which uses $$N - 1$$, use corrm() or corrx().

corrs.src