*DATA MINING SAS NOTES
*
*Box-Cox transformations and variable selection;


*Creating example data;
data regression_example;
call streaminit(5366);  
do i=1 to 1000;
	u=rand('UNIFORM');
	X1=10+20*rand('UNIFORM');
	X2=40+10*rand('UNIFORM');
	X3=500+100*rand('UNIFORM');
	epsilon=.1*rand("NORMAL");
	W=200+3*X1+4*X2+0.7*X3+epsilon;
	Y=W**2;
	output;
end;
run;

*Checking example data with glmselect;
proc glmselect data=regression_example;
model W=X1 X1*X1 X2 X3 ;
run;


*Performing a box-cox transformation to Y
*In general, Ytilde = (y^lambda-1)/lambda, if lambda != 0
*            Ytilde = log(Y), if lambda = 0;

ods graphics on;
proc transreg data=regression_example;
model boxcox(Y/lambda = -2 to 2 by .01) = Identity(X1 X2 X3);
output out=myoutput coefficients;
run;
ods graphics off;

proc print data=myoutput;
run;





*Tranforming Y using lambda obtained from Box-Cox procedure;
data regression_example;
call streaminit(5366);  
do i=1 to 1000;
	u=rand('UNIFORM');
	X1=10+20*rand('UNIFORM');
	X2=40+10*rand('UNIFORM');
	X3=500+100*rand('UNIFORM');
	epsilon=.1*rand("NORMAL");
	W=200+3*X1+4*X2+0.7*X3+epsilon;
	Y=W**2;
	Ytilde=(Y**0.5-1)/0.5;
	output;
end;
run;



*Refitting model to transformed Y;
proc glmselect data=regression_example;
model Ytilde=X1 X1*X1 X2 X3 ;
run;




*Creating data for performing a stepwise regression;
data regression_example;
call streaminit(5366);  
do i=1 to 1000;
	u=rand('UNIFORM');
	X1=10+20*rand('UNIFORM');
	X2=40+10*rand('UNIFORM');
	X3=500+100*rand('UNIFORM');
	X4=500+100*rand('UNIFORM');
	X5=500+100*rand('UNIFORM');
	X6=500+100*rand('UNIFORM');
	X7=500+100*rand('UNIFORM');
	X8=500+100*rand('UNIFORM');
	X9=500+100*rand('UNIFORM');
	X10=500+100*rand('UNIFORM');
	X11=500+100*rand('UNIFORM');
	X12=500+100*rand('UNIFORM');
	X13=500+100*rand('UNIFORM');
	X14=500+100*rand('UNIFORM');
	X15=500+100*rand('UNIFORM');
	X16=500+100*rand('UNIFORM');
	X17=500+100*rand('UNIFORM');
	X18=500+100*rand('UNIFORM');
	X19=500+100*rand('UNIFORM');
	X20=500+100*rand('UNIFORM');
	epsilon=.1*rand("NORMAL");
	Y=200+3*X1+4*X2+0.7*X3+epsilon;
	output;
end;
run;


*Typical regression;
proc reg data=regression_example;
model Y=X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20;
run;


*To generate the model statement, use the R code
temp=""
for(i in 1:20){
  temp=paste(temp,paste0("X",i))
}
temp
;


*Regression with stepwise variable selection;
proc glmselect data=regression_example;
model Y=X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20/selection=stepwise;
run;