Example 8.1: Correlation

General Statistics Examples

Example 8.1: Correlation

This example defines modules to compute correlation coefficients between numeric variables and standardized values for a set of data.

      /* Module to compute correlations  */
   start corr;
      n=nrow(x);                      /* number of observations */
      sum=x[+,] ;                        /* compute column sums */
      xpx=t(x)*x-t(sum)*sum/n;         /* compute sscp matrix   */
      s=diag(1/sqrt(vecdiag(xpx)));           /* scaling matrix */
      corr=s*xpx*s;                       /* correlation matrix */
      print "Correlation Matrix",,corr[rowname=nm colname=nm] ;
   finish corr;
 x
      /* Module to standardize data */
   start std;
      mean=x[+,] /n;                       /* means for columns */
      x=x-repeat(mean,n,1);            /* center x to mean zero */
      ss=x[##,] ;                 /* sum of squares for columns */
      std=sqrt(ss/(n-1));         /* standard deviation estimate*/
      x=x*diag(1/std);                  /* scaling to std dev 1 */
      print ,"Standardized Data",,X[colname=nm] ;
   finish std;

      /* Sample run */
   x = { 1 2 3,
         3 2 1,
         4 2 1,
         0 4 1,
        24 1 0,
         1 3 8};
   nm={age weight height};
   run corr;
   run std;

The results are shown below.

Correlation Matrix

CORR
	AGE	WEIGHT	HEIGHT
AGE	1	-0.717102	-0.436558
WEIGHT	-0.717102	1	0.3508232
HEIGHT	-0.436558	0.3508232	1

Standardized Data

X
AGE	WEIGHT	HEIGHT
-0.490116	-0.322749	0.2264554
-0.272287	-0.322749	-0.452911
-0.163372	-0.322749	-0.452911
-0.59903	1.6137431	-0.452911
2.0149206	-1.290994	-0.792594
-0.490116	0.6454972	1.924871

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