options ls=75 nocenter;
/* read in a table of data into variables */
data mileage;
input Y X;
cards;
22 35
20 35
28 40
31 40
37 45
38 45
41 50
39 50
34 55
37 55
27 60
30 60
;

proc means;

data cent_mi;
set mileage;
XX=X*X;
Xc=X-47.5;
XXc= Xc*Xc;
output;
run;

proc means;

/* model it, and show the solution */
title 'proc glm Y=Xc ';
proc glm;
model  Y=Xc /solution;
run;

/* model it, and show the solution */
title 'proc glm Y=Xc XXc';
proc glm;
model Y=Xc XXc /solution;
output out=qmile predicted=yhat;
run;

proc plot data=qmile;
title 'Problem 7-31A';
  plot y*x='Y'  yhat*x='P' / overlay;
run;

proc corr ;
title 'Problem 7.31g(1)Correlation from proc corr: X vs XX';
var X XX;
run;

proc corr ;
title 'Problem 7.31g(2): Correlation from proc corr: Xc vs XXc';
var Xc XXc;
run;