options ls=78;
title "PCA - Covariance Matrix - Places Rated";

 /* After reading in the places data, the (base 10) log transformations are taken.
  * This is an optional step and not required for the pca analysis.
  */

data places;
  infile "D:\Statistics\STAT 505\data\places.csv" firstobs=2 delimiter=',';
  input climate housing health crime trans educate arts recreate econ id;
  climate=log10(climate);
  housing=log10(housing);
  health=log10(health);
  crime=log10(crime);
  trans=log10(trans);
  educate=log10(educate);
  arts=log10(arts);
  recreate=log10(recreate);
  econ=log10(econ);
  run;

 /* The princomp procedure performs pca on the places data.
  * The cov option specifies results are calculated from the covariance
  * matrix, instead of the default correlation matrix.
  * The out=a option saves results to a data set named 'a'.
  */

proc princomp data=places cov out=a;
  var climate housing health crime trans educate arts recreate econ;
  run;

 /* The corr procedure is used to calculate pairwise correlations
  * between the first 3 principal components and the original variables.
  */

proc corr data=a;
  var prin1 prin2 prin3 climate housing health crime trans educate arts 
      recreate econ;
  run;

 /* The gplot procedure is used to plot the first 2 principal components.
  * axis1 and axis2 options set the plotting window size,
  * and these are then set to vertical and horizontal axes, respectively.
  */

proc gplot data=a;
  axis1 length=5 in;
  axis2 length=5 in;
  plot prin2*prin1 / vaxis=axis1 haxis=axis2;
  run;