/*start by setting the graphics options --Note that names of windows fonts are given in quotes*/
goptions reset=global gunit=in 
         ftitle="garamond" ftext="garamond" htitle=.5 htext=.5;


/* read in some data  -- look familiar? */

data example;
input northing easting z;
cards;
1 1  1
1 2  5
1 3  10
1 4  6
1 5  2 
1 6  1
1 7  4
1 8  9
1 9  7
;
proc print;


Title1 'The Data';
proc gplot data=example;
symbol1 v=dot h=.3 cv=grey; 
plot z*easting ;
run;

/*linear regression */

Title1 'The Linear Fit: Degree=1';
Proc glm data = example;
model z=easting / solution;
output out=pred p=predicted r=residual;


proc gplot data=pred;
symbol1 v=dot h=.3 cv=grey ; 
symbol2 v= i=spline l=5 w=2 color=red; 
plot 	z*easting= 1 
		predicted*easting= 2 / overlay;
run;


/*Quadratic */

Title1 'The Quadratic Fit: Degree=2';
Proc glm data = example;
model z=easting easting*easting/ solution;
output out=pred p=predicted r=residual;


proc gplot data=pred;

plot 	z*easting= 1 
		predicted*easting= 2 / overlay;
run;

/*cubic*/

Title1 'The Cubic Fit: Degree=3';
Proc glm data = example;
model z=easting easting*easting  easting*easting*easting  / solution;
output out=pred p=predicted r=residual;


proc gplot data=pred;
plot 	z*easting= 1 
		predicted*easting= 2 / overlay;
run;


/*quartic*/

Title1 'The Quartic Fit: Degree=4';
Proc glm data = example;
model z=easting easting*easting  easting*easting*easting easting*easting*easting*easting   / solution;
output out=pred p=predicted r=residual;

proc gplot data=pred;
plot 	z*easting= 1 
		predicted*easting= 2 / overlay;
run;



/*quintic*/

Title1 'The Quintic Fit: Degree=5';
Proc glm data = example;
model z=easting easting*easting  easting*easting*easting easting*easting*easting*easting  

easting*easting*easting*easting*easting   / solution;
output out=pred p=predicted r=residual;

proc gplot data=pred;

plot 	z*easting= 1 
		predicted*easting= 2 / overlay;
run;


/*loess*/
Title1 'Loess: lambda=2, alpha chosen by GCV';
proc loess data =example;
ods Output  OutputStatistics=StatOut;
model z = easting / degree=2  select=gcv ; 

proc gplot data=StatOut;;

plot 	depvar*easting= 1 
		pred*easting= 2 / overlay;
run;


/*loess*/
Title1 'Loess: lambda=1, alpha chosen by GCV';
proc loess data =example;
ods Output  OutputStatistics=StatOut;
model z = easting / degree=1  select=gcv ; 

proc gplot data=StatOut;;
plot 	depvar*easting= 1 
		pred*easting= 2 / overlay;
run;