ST 590G -- Computation for Data Analysis

  Third Assignment -- due Thursday, 25 October 2011

  Determining whether a regression model is correct is difficult unless
  the sample include replication -- that is, observations with the same 
  design points.  Here we are looking at another, somewhat ad hoc, approach
  for cases where there are no replicates.  This approach is a variation 
  on cross-validation, which has been successfully employed as a tuning
  parameter when trading off the complexity of a model and its fit.

  Your assignment is to write a macro to compute suitable five-fold cross-
  validation statistics for testing lack of fit.  Given a parameter NREP
  number of replications, select a random subset of four-fifths of the 
  observations computing estimates of the regression parameters.  Using 
  those estimates, compute forecasts for the remaining one fifth of the 
  observations.  Compare the forecasts with the observations by computing
     d(i) = (observed Y(i) - forecast Y(i))/standard error of forecast 
  and then compute
     V = SUM d(i)^2 / estimate of variance from regression model
  If we have the correct model, V should have a chi-square distribution
  with degrees of freedom equal to the number of observations in the 
  witheld one fifth of the data.  Have the macro produce only the results
  from a proc univariate analysis of NREP values of V's.  Write appropriate
  titles for the output, for example, 'this should look like a chi-square
  distribution with 57 degrees of freedom.'  Also, clean up as a part of 
  the macro by deleting datasets that you created.  (Hmmm, you might want 
  to be careful to use atypical dataset names.)

  KISS -- so write the macro for just simple linear regression.
  (If you can easily extend it to an arbitrary regression model -- bonus!)

  The arguments to your macro should be 
    a) the name of the dataset
    b) the names of the two variables (Y and X)
    c) the number of replications.
  
  Demonstrate your macro on the salary data in the October directory.
  
  ***Also, email your macro code to be as flat file attachment.***