/* MathReg1.sas  */
%include '/home/brunner0/441s20/readmath2b.sas'; 
/* readmath2b has dummy variable definitions 
        e1-e4,e6 for ethnic (Reference category is East Indian)
        gender=1 for Female
        mtongue=1 for English
        c1-c3: c1 = 'Catch-up' c2 = 'Mainstream' c3 = 'Elite'   */

title2 'Variable Selection for Predicting Grade';

proc freq;
     title3 'Check dummy variables';
     tables sex*gender / norow nocol nopercent missing;
     tables tongue*mtongue / norow nocol nopercent missing;
     tables (e1-e4 e6) * ethnic / norow nocol nopercent missing;
     tables (c1-c3) * course / norow nocol nopercent missing;

proc reg plots = none; /* Suppress diagnostic plots for now*/
     title3 'Model A: Predict University Calculus Grade from HS Information';
     model grade = hsgpa hscalc hsengl;

/* It is very interesting to know what proportion of the remaining
   variation is explained by each variable, controlling for the other two. 
   F = t-squared, and
                       a = sF/(n-p + sF)
*/

proc iml;
     title3 'Proportion of remaining variation for HS information';
     n = 323; p = 4; s = 1;
     print "hsgpa controlling for hscalc and hsengl";
     t = 8.00; F = t**2;  a = s*F/(n-p + s*F);
     print a;

     print "hscalc controlling for hsgpa and hsengl";
     t = 3.14; F = t**2;  a = s*F/(n-p + s*F);
     print a;

     print "hsengl controlling for hsgpa and hscalc";
     t = -3.26; F = t**2;  a = s*F/(n-p + s*F);
     print a;
     
proc reg plots = none;
     title3 'Model B: Predict University Calculus Grade from Diagnostic Test';
     model grade = precalc calc;

proc reg plots = none;
     title3 'Model C: Do the diagnostic test and HS info both contribute?';
     model grade = hsgpa hscalc hsengl precalc calc;
     Diagnostic_Test:  test  precalc=calc=0;
     HS_Information:   test  hsgpa=hscalc=hsengl=0;

proc iml;
     title3 'Proportion of remaining variation explained by diagnostic test';
     print "Precalc and calc controlling for hsgpa hscalc hsengl";
     n = 289; p = 6; s = 2; F = 8.28;
     a = s*F/(n-p + s*F); print a;

proc iml;
     title3 'Proportion of remaining variation explained by HS info';
     print "Hsgpa hscalc hsengl controlling for precalc and calc";
     n = 289; p = 6; s = 3; F = 46.97;
     a = s*F/(n-p + s*F); print a;

proc reg plots = none;
     title3 'Model D: See if Course makes a contribution';
     model grade = hsgpa hscalc hsengl precalc calc c1 c3;
     Course: test c1=c3=0;
     Diagnostic_Test:  test  precalc=calc=0;

proc glm;
     title3 'Model D again with proc glm';
     class course;
     model grade =  hsgpa hscalc hsengl precalc calc course;
     contrast 'Replicate Test of Course' course 1 -1  0,
                                         course 0  1 -1;
     contrast 'Diagnostic Test F = 9.06' precalc 1, calc 1;

proc reg plots = none;
     title3 'Model E: Include Language, Sex and Ethnic Background';
     model grade = hsgpa hscalc hsengl precalc calc 
                   mtongue gender e1-e4 e6;
     TroubleVars: test mtongue=gender=e1=e2=e3=e4=e6=0;
     Nationality: test e1=e2=e3=e4=e6=0;

proc reg plots = none;
     title3 'Model F: Discarding Gender and Nationality';
     model grade = hsgpa hscalc hsengl precalc calc mtongue;
     EnglishTongue: test hsengl=mtongue=0;

proc iml;
     title3 'Proportion of remaining variation explained by mother tongue';
     print "Mtongue controlling for hsgpa hscalc hsengl precalc calc";
     n = 287; p = 7; s = 1; t = -2.23 ; F = t**2;
     a = s*F/(n-p + s*F); print a;

proc reg plots = none;
     title3 'Model G:  Drop mtongue and calc';
     title4 'Compare  R-Square = 0.4556, Adj R-Sq = 0.4460 From Model 3';
     model grade = hsgpa hscalc hsengl precalc;

proc iml;
     title3 'Proportion of remaining variation explained by Pre-calculus';
     print "precalc controlling for hsgpa hscalc hsengl";
     n = 289; p = 5; s = 1; t = 3.63 ; F = t**2;
     a = s*F/(n-p + s*F); print a;

proc reg plots = none;
     title3 'Model H: Combine precalc and calc instead of dropping calc';
     title4 'Compare  R-Square = 0.4492 from Model G';
     model grade = hsgpa hscalc hsengl totscore;

proc iml;
     title3 'Proportion of remaining variation explained by Pre-calculus';
     print "totscore controlling for hsgpa hscalc hsengl";
     n = 289; p = 5; s = 1; t = 3.92 ; F = t**2;
     a = s*F/(n-p + s*F); print a;
     print "For prediction, I am happy with Model H: hsgpa hscalc hsengl totscore";

proc reg plots = none;
     title3 'Model I: Same as Model H but including Mother Tongue';
     model grade = hsgpa hscalc hsengl totscore mtongue;
/* A slightly better model except for the lawsuit. */

proc reg plots = none;
     title3 'Try automatic (stepwise) selection';
     model grade = hsgpa hscalc hsengl precalc calc totscore
                   mtongue gender e1-e4 e6 
                   / selection = stepwise slentry = 0.05 slstay = 0.05 ;
                   /* Default slentry = slstay = 0.15 */
quit;