[Delphi] Linear and Quadratic Regression (just for self documentation)

The code below have the plots and graphs (linear and quadratic regression) included

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, Grids, ExtCtrls, StdCtrls;

type
  TForm1 = class(TForm)
    StringGrid1: TStringGrid;
    Image1: TImage;
    Memo1: TMemo;
    procedure awal;
    procedure datamentah;
    procedure plotdata;
    procedure regresi;
    procedure kuadratis;
    procedure plotregresi;
    function f(x:real):real;
    function fk(x:real):real;
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

const n=40; skala=3;
var
  Form1: TForm1;
  x0,y0:integer;                              x,y:array[-n..n]of real;
  a,b:real;                                   c:array[1..3]of real;
  matrik:array[1..3,1..4]of real;
implementation

{$R *.dfm}
procedure tform1.kuadratis;
var sxi,sxi2,sxi3,sxi4,syi,syixi,syixi2:real;
i,j,k:integer;                                jml,simpan:real;
begin
sxi:=0;sxi2:=0;sxi3:=0;sxi4:=0;               syi:=0;syixi:=0;syixi2:=0;
{sigma xi} {sigma xi kuadrat}                 {sigma xi pangkat3} {sigma xi pangkat4}
{sigma yi} {sigma yi*xi}                      {sigma yi* xi*xi }
for i:=1 to n do begin
  sxi:=sxi+x[i];                              sxi2:=sxi2+x[i]*x[i];
  sxi3:=sxi3+x[i]*x[i]*x[i];                  sxi4:=sxi4+x[i]*x[i]*x[i]*x[i];
  syi:=syi+y[i];                              syixi:=syixi+y[i]*x[i];
  syixi2:=syixi2+                             y[i]*x[i]*x[i];
end;
{isi matrik}
matrik[1,1]:=n;                               matrik[1,2]:=sxi;
matrik[1,3]:=sxi2;                            matrik[1,4]:=syi;
matrik[2,1]:=sxi;                             matrik[2,2]:=sxi2;
matrik[2,3]:=sxi3;                            matrik[2,4]:=syixi;
matrik[3,1]:=sxi2;                            matrik[3,2]:=sxi3;
matrik[3,3]:=sxi4;                            matrik[3,4]:=syixi2;
{gaus naif}
for k:= 1 to 3 do begin
  for i:= k+1 to 3 do begin
    simpan:=matrik[i,k];
      if simpan=0 then begin end
        else begin
         for j:=k to 4 do
           matrik[i,j]:=
             matrik[i,j]/
              simpan*
                matrik[k,k]-
                  matrik[k,j];
                    end;
                      end;
                        end;
{subtitusi}
c[3]:=matrik[3,4]/matrik[3,3];for i:=2 downto 1 do begin jml:=0;for j:=i+1
to 3
do jml:=jml+matrik[i,j]*c[j]; c[i]:=(matrik[i,4]-jml)/matrik[i,i];end;
memo1.Lines.Append('c[1] = '+ floattostr(c[1]));
memo1.Lines.Append('c[2] = '+ floattostr(c[2]));
memo1.Lines.Append('c[3] = '+ floattostr(c[3]));
{plot kuadratis}
image1.Canvas.Pen.Color:=clred;
image1.Canvas.MoveTo(x0+round(x[-n]),y0-round(skala*fk(x[-n])));
for i:=-n to n do begin
image1.Canvas.lineto(x0+round(x[i]),y0-round(skala*fk(x[i])));
end;
end;

function tform1.fk(x:real):real;
begin
  fk:=c[1]+c[2]*x+c[3]*x*x;
end;

procedure tform1.regresi;
var i:integer;                                xix,xixx,rx,ry:real;
begin
  rx:=0;ry:=0;
  for i:=1 to n do begin
    rx:=rx+x[i];                              ry:=ry+y[i];
  end;
  rx:=rx/n;                                   ry:=ry/n;
  memo1.Lines.Append('rx = '+floattostr(rx)); memo1.Lines.Append('ry = '+floattostr(ry));
  xix:=0;                                     xixx:=0;
  for i:=1 to n do begin
    xix:=xix+(x[i]-rx)*(y[i]-ry);             xixx:=xixx+(x[i]-rx)*(x[i]-rx);
  end;
  b:=xix/xixx;                                memo1.Lines.Append('b = '+floattostr(b));
  a:=ry-b*rx;                                 memo1.Lines.Append('a = '+floattostr(a));
end;

procedure tform1.awal;
begin
  randomize;                                  memo1.Text:='';
  stringgrid1.Cells[0,0]:='x';                stringgrid1.Cells[1,0]:='y';
  stringgrid1.RowCount:=2;
  datamentah;
  plotdata;
  regresi;
  plotregresi;
  kuadratis;
end;

procedure tform1.plotregresi;
var px,py:real;
begin
  px:=-2*n;                                    py:=a+b*(-2*n);
  image1.Canvas.pen.Color:=cllime;
  image1.Canvas.MoveTo(x0+round(px),           y0-skala*round(py));
  px:=2*n;                                     py:=a+b*(2*n);
  image1.Canvas.lineTo(x0+round(px),y0-skala*  round(py));
  memo1.Lines.Append('fungsi regresi: y ='+    floattostrf(a,ffGeneral,2,4)+' + '+
  floattostrf(b,                               ffGeneral,2,4)+' x');
end;

procedure tform1.plotdata;
var i:integer;
begin
  x0:=round(image1.Width/2);                  y0:=round(image1.Height/2);
  image1.Canvas.MoveTo(0,y0);                 image1.Canvas.LineTo(image1.Width,y0);
  image1.Canvas.MoveTo(x0,0);                 image1.Canvas.LineTo(x0,image1.Height);
  for i:=-n to n do begin
    image1.Canvas.Pixels[x0+round(x[i]),y0-round(skala*y[i])]:=clblue;
  end;
end;
procedure tform1.datamentah;
var i:integer;
begin
  stringgrid1.RowCount:=2*n+1;
  for i:=-n to n do begin
    x[i]:=i;                                  y[i]:=f(x[i]);
    stringgrid1.Cells[0,i+n+1]:=floattostr(x[i]);
    stringgrid1.Cells[1,i+n+1]:=floattostr(y[i]);
  end;
end;

function tform1.f(x:real):real;
begin
  f:=x*x/32+random(20)-10;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  awal;
end;

end.