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options ls=78;   /*This sets the max number of lines per page to 78.*/
title "Example: Nutrient Intake Data - Generalized Variance";   /*This sets a title that will 
appear on each page of the output until it's changed.*/
data nutrient;   /*This defines a data set called 'nutrient'.*/
  infile "D:\Statistics\STAT 505\data\nutrient.csv" firstobs=2 delimiter=',';   /*SAS will look in this path for the 
  nutrient.csv file.*/
  input id calcium iron protein a c;   /*This is where we provide names for the variables 
  in order of the columns in the data set. If any were categorical (not the case here), 
  we would need to put a '$' character after its name.*/
  run;   
proc iml;   /*The iml procedure allows for many general calculations to be made, including 
matrix operations.*/
  start genvar;   /*This defines a SAS module that can be called to compute the 
  generalized variance. The lines of code below are executed when 'genvar' is called, 
  and both the sample covariance matrix and the generalized variance are printed.*/
    one=j(nrow(x),1,1);   /*This defines a column vector of 1s. The size is determined by 
    'x', which is a variable that is defined outside the module below.*/
    ident=i(nrow(x));   /*This creates an identity matrix with the same number of rows 
    as x.*/
    s=x`*(ident-one*one`/nrow(x))*x/(nrow(x)-1.0);   /*This is the sample covariance 
    matrix, which is an unbiased estimate of the population covariance matrix.*/
    genvar=det(s);   /*The generalized variance is the determinant of the sample 
    covariance matrix.*/
    print s genvar;   /*This is the statement that prints both the sample covariance 
    matrix and the generalized variance.*/
  finish;   /*This ends the genmod module definition. The module hasn't run yet and 
  won't be called until we define the 'x' argument below.*/
  use nutrient;   /*This makes the variables from the 'nutrient' data set available 
  for use in this iml environment.*/
  read all var{calcium iron protein a c} into x;   /*This creates a vector x 
  consisting of the variables specified. This vector is what will be used in the 
  'genvar' module defined above.*/
  run genvar;   /*This statements calls the 'genvar' module, which we defined above.*/