/* MathReg2.sas  */
%include '/folders/myfolders/441s16/Lecture/readmath2b.sas'; 
title2 'Residual analysis';

proc reg plots(only) = ResidualPlot; 
     title3 'Model H: hsgpa hscalc hsengl totscore';
     model grade = hsgpa hscalc hsengl totscore;
     output out = Explor predicted = yhat 
                         residual  = resid
                         rstudent  = delstud; 
                                  /* Deleted Studentized Residual */

/* Could have included LCL and UCL for upper and lower limits of a 
   95% prediction interval for each case in the file */


/* What is a big (Studentized deleted) residual? If the model is correct,
   each one has a t distribution with n-p-1 = 283 df (practically standard 
   normal), so the Studentized deleted residual can be treated directly as
   a t-test statistic. Values that are too big in absolute value will cause
   H0: mu=0 to be rejected. Tests are NOT independent, but use a Bonferroni
   correction for n = 289 tests. Get the critical value from proc iml. */

proc iml;
     title3 'Critical value for Joint t-test on Studentized Residuals';
     Alpha = 0.05/289; print Alpha;
     Critval = tinv(1-Alpha/2,283); print Critval;

proc univariate normal plot;
     var delstud;

/* Tests for normality indicate residuals are not normal. No st resids
greater than critical value. Next, a few more plots. */

proc sgplot;
     title3 'Plot of Y-hat by Y';
     scatter y=grade x=yhat;

proc sgplot;
     title3 'Calculus sub-test by deleted studentized residual';
     scatter x=calc y=delstud;

proc sgplot;
     title3 'Pre-calculus sub-test by deleted studentized residual';
     scatter x=precalc y=delstud;
     
proc sgplot;
     title3 'Mother tongue by deleted studentized residual';
     scatter x=mtongue y=delstud;