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().

Source

corrs.src

See also

Functions momentd(), corrm(), corrx(), varCovX(), varCovM()