Double Checking Covariance Matrix
Sample Covariance Matrix
Sample Covariance Matrix

THE DATASET XX WITH FIVE COLUMN VECTORS IS

XX
5.0000 4.0000 1.0000
7.0000 9.0000 7.0000
0.0000 1.0000 1.0000
12.0000 -2.0000 1.0000
7.0000 6.0000 5.0000

THE COVARIANCE MATRIX OF THE 5 COLUMNS OF X IS

COVAR
18.7000 -2.6500 2.0000
-2.6500 18.3000 10.5000
2.0000 10.5000 8.0000

Double Checking Covariance Matrix

The CORR Procedure

3 Variables: x1 x2 x3

Covariance Matrix, DF = 4
  x1 x2 x3
x1 18.70000000 -2.65000000 2.00000000
x2 -2.65000000 18.30000000 10.50000000
x3 2.00000000 10.50000000 8.00000000

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
x1 5 6.20000 4.32435 31.00000 0 12.00000
x2 5 3.60000 4.27785 18.00000 -2.00000 9.00000
x3 5 3.00000 2.82843 15.00000 1.00000 7.00000

Pearson Correlation Coefficients, N = 5
  x1 x2 x3
x1 1.00000 -0.14325 0.16352
x2 -0.14325 1.00000 0.86780
x3 0.16352 0.86780 1.00000

Double Checking Covariance Matrix
Sample Covariance Matrix

The PRINCOMP Procedure

Observations 5
Variables 3

Simple Statistics
  x1 x2 x3
Mean 6.200000000 3.600000000 3.000000000
StD 4.324349662 4.277849927 2.828427125

Covariance Matrix
  x1 x2 x3
x1 18.70000000 -2.65000000 2.00000000
x2 -2.65000000 18.30000000 10.50000000
x3 2.00000000 10.50000000 8.00000000

Total Variance 45

Eigenvalues of the Covariance Matrix
  Eigenvalue Difference Proportion Cumulative
1 25.0823156 6.0778841 0.5574 0.5574
2 19.0044314 18.0911785 0.4223 0.9797
3 0.9132530   0.0203 1.0000

Eigenvectors
  Prin1 Prin2 Prin3
x1 -.195382 0.965491 -.172199
x2 0.845551 0.076880 -.528331
x3 0.496860 0.248829 0.831393