/* Custom-made function Overfit */
/* Data from Holton(2003)"Value-at-Risk" */
new; cls;
let data[10,2]=
1.1  2.14
1.4  2.60
2.5  1.15
2.7  1.19
3.2  1.88
3.6  1.55
4.1  2.65
4.3  3.80
4.5  4.46
4.9  6.35
;
x=data[.,1]; y=data[.,2];
start={0,0,0}; 
fn function(b)=b[1]+exp(b[2]*x)+b[3]*x;          /* You can set this. */


fn fct(b)=(y-function(b))'(y-function(b));
screen off;
   { b,f,g,ret }=QNewton( &fct,start );
screen on;
print "b=" b;
points=1000;
xx=seqa(minc(x),(maxc(x)-minc(x))/(points-1),points-1)|maxc(x);
/* graph */
   library pgraph;
   graphset;
   pqgwin auto;
   begwind;
   window(1,1,0);
   scale(-0.05*(maxc(x)-minc(x))+minc(x)|maxc(x)+0.05*(maxc(x)-minc(x)),-0.25*(maxc(y)-minc(y))+minc(y)|maxc(y)+0.25*(maxc(y)-minc(y)));
   setwind(1);
      title("nonlinear function");
      _plctrl=-1;
      _pcolor=15;
      _psymsiz=1;
      xy(x,y);
   setwind(1);
      _plctrl=0;
      _pcolor=10;
      x=xx;              /* switch data to x's sequence to draw a curve */
      xy(xx,function(b));
   endwind;