# 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

Returns:

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 corrms() and corrxs() computes the sample correlation matrix. For the population correlation matrix, use corrm() or corrx().

corrs.src