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git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7881 8e941d3f-bd1b-0410-a28a-d453659cc2b4
371 lines
12 KiB
ObjectPascal
371 lines
12 KiB
ObjectPascal
unit CorSimUnit;
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{$mode objfpc}{$H+}
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interface
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uses
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Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs,
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ExtCtrls, StdCtrls, Globals, OutPutUnit, Math;
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type
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{ TCorSimFrm }
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TCorSimFrm = class(TForm)
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Nobs: TEdit;
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Image1: TImage;
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Label6: TLabel;
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ReturnBtn: TButton;
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ComputeBtn: TButton;
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Corr: TEdit;
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Label5: TLabel;
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SDY: TEdit;
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Label4: TLabel;
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SDX: TEdit;
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Label3: TLabel;
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MeanY: TEdit;
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Label2: TLabel;
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MeanX: TEdit;
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Label1: TLabel;
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Panel1: TPanel;
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procedure ComputeBtnClick(Sender: TObject);
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procedure CorrKeyPress(Sender: TObject; var Key: char);
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procedure FormShow(Sender: TObject);
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procedure MeanXKeyPress(Sender: TObject; var Key: char);
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procedure MeanYKeyPress(Sender: TObject; var Key: char);
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procedure NobsKeyPress(Sender: TObject; var Key: char);
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procedure SDXKeyPress(Sender: TObject; var Key: char);
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procedure SDYKeyPress(Sender: TObject; var Key: char);
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private
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{ private declarations }
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xmean, ymean, xsd, ysd, corxy, corsqr, yvariance, predvar : double;
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errvariance, stderror, b, constant, newxmean, newymean : double;
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newxsd, newysd, newcorr, randomerror, newb, newconstant : double;
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x, y : DblDyneVec;
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freqx, freqy : IntDyneVec;
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N : integer;
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procedure plot(Sender: TObject);
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public
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{ public declarations }
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end;
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var
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CorSimFrm: TCorSimFrm;
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implementation
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{ TCorSimFrm }
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procedure TCorSimFrm.MeanXKeyPress(Sender: TObject; var Key: char);
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begin
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if Ord(Key) = 13 then MeanY.SetFocus;
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end;
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procedure TCorSimFrm.CorrKeyPress(Sender: TObject; var Key: char);
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begin
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if Ord(Key) = 13 then Nobs.SetFocus;
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end;
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procedure TCorSimFrm.ComputeBtnClick(Sender: TObject);
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var
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outline : string;
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i : integer;
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begin
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N := StrToInt(NObs.Text);
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xmean := StrToFloat(MeanX.Text);
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ymean := StrToFloat(MeanY.Text);
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xsd := StrToFloat(SDX.Text);
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ysd := StrToFloat(SDY.Text);
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corxy := StrToFloat(Corr.Text);
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Randomize;
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SetLength(freqx,N + 1);
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SetLength(freqy,N + 1);
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SetLength(x,N + 1);
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SetLength(y,N + 1);
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// generate x and y data observations
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corsqr := corxy * corxy;
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yvariance := ysd * ysd;
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predvar := corsqr * yvariance;
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errvariance := yvariance - predvar;
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stderror := sqrt(errvariance);
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b := corxy * (ysd / xsd);
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constant := ymean - (b * xmean);
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newxmean := 0.0;
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newymean := 0.0;
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newxsd := 0.0;
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newysd := 0.0;
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newcorr := 0.0;
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for i := 1 to N do
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begin
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x[i] := RandG(xmean,xsd);
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randomerror := RandG(0.0,stderror);
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y[i] := (b * x[i]) + constant + randomerror;
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newxmean := newxmean + x[i];
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newymean := newymean + y[i];
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newxsd := newxsd + (x[i] * x[i]);
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newysd := newysd + (y[i] * y[i]);
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newcorr := newcorr + (x[i] * y[i]);
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end;
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newxsd := newxsd - ((newxmean * newxmean) / N);
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newxsd := newxsd / (N - 1.0);
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newxsd := sqrt(newxsd);
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newysd := newysd - ((newymean * newymean) / N);
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newysd := newysd / (N - 1.0);
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newysd := sqrt(newysd);
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newcorr := newcorr - ((newxmean * newymean) / N);
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newcorr := newcorr / (N - 1.0);
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newcorr := newcorr / (newxsd * newysd);
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newxmean := newxmean / N;
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newymean := newymean / N;
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newb := newcorr * (newysd / newxsd);
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newconstant := newymean - (newb * newxmean);
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OutPutFrm.RichEdit.Lines.Clear;
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outline := 'POPULATION PARAMETERS FOR THE SIMULATION';
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OutPutFrm.RichEdit.Lines.Add(outline);
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OutPutFrm.RichEdit.Lines.Add('');
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outline := format('Mean X := %8.3f, Std. Dev. X := %8.3f',[xmean, xsd]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Mean Y := %8.3f, Std. Dev. Y := %8.3f',[ymean, ysd]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Product-Moment Correlation := %8.3f',[corxy]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Regression line slope := %8.3f, constant := %8.3f',
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[b, constant]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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OutPutFrm.RichEdit.Lines.Add('');
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OutPutFrm.RichEdit.Lines.Add('');
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outline := format('SAMPLE STATISTICS FOR %d OBSERVATIONS FROM THE POPULATION',[N]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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OutPutFrm.RichEdit.Lines.Add('');
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outline := format('Mean X := %8.3f, Std. Dev. X := %8.3f',[newxmean, newxsd]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Mean Y := %8.3f, Std. Dev. Y := %8.3f',[newymean, newysd]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Product-Moment Correlation := %8.3f',[newcorr]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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outline := format('Regression line slope := %8.3f, constant := %8.3f',
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[newb, newconstant]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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OutPutFrm.RichEdit.Lines.Add('');
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OutPutFrm.RichEdit.Lines.Add('Pair No. X Y');
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for i := 1 to N do
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begin
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outline := format(' %3d %9.3f %9.3f',[i,x[i],y[i]]);
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OutPutFrm.RichEdit.Lines.Add(outline);
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end;
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OutPutFrm.ShowModal;
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plot(self);
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freqx := nil;
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freqy := nil;
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x := nil;
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y := nil;
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ReturnBtn.SetFocus;
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end;
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procedure TCorSimFrm.FormShow(Sender: TObject);
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begin
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CorSimFrm.Image1.Canvas.Pen.Color := clBlack;
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CorSimFrm.Image1.Canvas.Brush.Color := clWhite;
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CorSimFrm.Image1.Canvas.Clear;
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CorSimFrm.Image1.Canvas.FloodFill(1,1,clWhite,fsborder);
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MeanX.Text := '100';
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MeanY.Text := '100';
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SDX.Text := '15';
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SDY.Text := '15';
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Corr.Text := '.8';
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Nobs.Text := '100';
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end;
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procedure TCorSimFrm.MeanYKeyPress(Sender: TObject; var Key: char);
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begin
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if Ord(Key) = 13 then SDX.SetFocus;
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end;
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procedure TCorSimFrm.NobsKeyPress(Sender: TObject; var Key: char);
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begin
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if Ord(Key) = 13 then ComputeBtn.SetFocus;
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end;
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procedure TCorSimFrm.SDXKeyPress(Sender: TObject; var Key: char);
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begin
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if Ord(Key) = 13 then SDY.SetFocus;
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end;
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procedure TCorSimFrm.SDYKeyPress(Sender: TObject; var Key: char);
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begin
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if Ord(Key) = 13 then Corr.SetFocus;
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end;
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procedure TCorSimFrm.plot(Sender: TObject);
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var
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minx, maxx, miny, maxy, xincrement, yincrement : double;
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predy1, predy2, lowerx, upperx, frange, prop : double;
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charlabel : string;
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xpos, ypos, xpos1, ypos1, xpos2, ypos2 : integer;
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i, winwidth, winheight, xoffset, yoffset, xaxislong, yaxislong : integer;
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j, xspacing, yspacing, labelwidth, minfreq, maxfreq : integer;
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flength, theight, lowery, uppery : integer;
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begin
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// get min and max of x and y points
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minx := x[1];
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maxx := minx;
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miny := y[1];
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maxy := miny;
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for i := 1 to N do
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begin
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if (minx > x[i]) then minx := x[i];
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if (maxx < x[i]) then maxx := x[i];
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if (miny > y[i]) then miny := y[i];
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if (maxy < y[i]) then maxy := y[i];
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end;
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xincrement := (maxx - minx) / 10;
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yincrement := (maxy - miny) / 10;
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winwidth := CorSimFrm.Image1.Width;
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winheight := CorSimFrm.Image1.Height;
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xoffset := winwidth div 5;
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yoffset := winheight div 5;
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xaxislong := winwidth - xoffset- winwidth div 10;
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yaxislong := winheight - yoffset - winheight div 10;
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Image1.Canvas.Pen.Color := clBlack;
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Image1.Canvas.MoveTo(xoffset,yaxislong);
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Image1.Canvas.LineTo(winwidth,yaxislong);
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Image1.Canvas.MoveTo(xoffset,yaxislong);
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Image1.Canvas.LineTo(xoffset,0);
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xspacing := xaxislong div 10;
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yspacing := yaxislong div 10;
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// do xaxis
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for i := 0 to 11 do
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begin
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Image1.Canvas.MoveTo(xoffset + (i * xspacing),yaxislong);
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Image1.Canvas.LineTo(xoffset + (i * xspacing),yaxislong + 10);
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charlabel := format('%8.3f',[minx + (i * xincrement)]);
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labelwidth := Image1.Canvas.TextWidth(charlabel);
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xpos := xoffset + (i * xspacing)-labelwidth div 2;
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ypos := yaxislong + 12;
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Image1.Canvas.TextOut(xpos,ypos,charlabel);
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end;
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// do yaxis
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for i := 0 to 11 do
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begin
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Image1.Canvas.MoveTo(xoffset, yaxislong - (i * yspacing));
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Image1.Canvas.LineTo(xoffset-10,yaxislong - (i * yspacing));
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charlabel := format('%8.3f',[miny + (i * yincrement)]);
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labelwidth := Image1.Canvas.TextWidth(charlabel);
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xpos := xoffset-10-labelwidth;
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ypos := yaxislong - (i * yspacing);
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Image1.Canvas.TextOut(xpos,ypos,charlabel);
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end;
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// plot points
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Image1.Canvas.Pen.Color := clRed;
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for i := 1 to N do
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begin
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xpos := round(xoffset + ((x[i] - minx) / (maxx - minx) * xaxislong));
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ypos := round(yaxislong - ((y[i] - miny) / (maxy - miny) * yaxislong));
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Image1.Canvas.Ellipse(xpos,ypos,xpos+5,ypos+5);
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end;
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// draw regression line
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Image1.Canvas.Pen.Color := clBlack;
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predy1 := newb * minx + newconstant;
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predy2 := newb * maxx + newconstant;
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xpos1 := xoffset;
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xpos2 := xoffset + xaxislong;
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ypos1 := round(yaxislong - ((predy1 - miny) / (maxy - miny) * yaxislong));
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ypos2 := round(yaxislong - ((predy2 - miny) / (maxy - miny) * yaxislong));
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Image1.Canvas.MoveTo(xpos1,ypos1);
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Image1.Canvas.LineTo(xpos2,ypos2);
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// do x frequency distribution
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xincrement := (maxx-minx) / 50.0;
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xspacing := xaxislong div 50;
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for j := 1 to 51 do freqx[j] := 0;
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for i := 1 to N do
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begin
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for j := 1 to 51 do
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begin
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lowerx := minx + (j * xincrement);
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upperx := minx + ((j+1) * xincrement);
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if ((x[i] >= lowerx) and (x[i] < upperx)) then freqx[j] := freqx[j] + 1;
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end;
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end;
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// plot the x frequencies
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minfreq := N;
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maxfreq := 0;
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for j := 1 to 51 do
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begin
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if (freqx[j] > maxfreq) then maxfreq := freqx[j];
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if (freqx[j] < minfreq) then minfreq := freqx[j];
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end;
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flength := winheight - (yaxislong + 25) - Panel1.Height;
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for j := 1 to 51 do
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begin
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xpos := xoffset + (j * xspacing);
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ypos1 := round(yaxislong + 25 +
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((freqx[j] - minfreq)/ (maxfreq-minfreq) * (flength)));
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ypos2 := yaxislong + 25;
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Image1.Canvas.MoveTo(xpos,ypos1);
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Image1.Canvas.LineTo(xpos,ypos2);
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end;
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Image1.Canvas.MoveTo(xoffset,yaxislong+25);
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Image1.Canvas.LineTo(winwidth,yaxislong+25);
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xpos := 20;
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ypos := yaxislong+30;
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Image1.Canvas.TextOut(xpos,ypos,'X DISTRIBUTION');
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theight := Image1.Canvas.TextHeight('X');
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ypos := ypos + theight;
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charlabel := format('correlation := %6.3f',[newcorr]);
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Image1.Canvas.TextOut(xpos,ypos,charlabel);
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ypos := ypos + theight;
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charlabel := format('Mean X := %8.3f, Mean Y := %8.3f',[newxmean, newymean]);
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Image1.Canvas.TextOut(xpos,ypos,charlabel);
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charlabel := format('SD X := %8.3f, SD Y := %8.3f',[newxsd, newysd]);
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ypos := ypos + theight;
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Image1.Canvas.TextOut(xpos,ypos,charlabel);
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// do y frequency distribution
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yincrement := (maxy-miny) / 50.0;
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yspacing := yaxislong div 50;
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for j := 1 to 51 do freqy[j] := 0;
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for i := 1 to N do
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begin
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for j := 1 to 51 do
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begin
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lowery := round(miny + (j * yincrement));
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uppery := round(miny + ((j+1) * yincrement));
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if ((y[i] >= lowery) and (y[i] < uppery)) then freqy[j] := freqy[j] + 1;
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end;
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end;
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// plot the y frequencies
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minfreq := N;
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maxfreq := 0;
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for j := 1 to 51 do
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begin
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if (freqy[j] > maxfreq) then maxfreq := freqy[j];
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if (freqy[j] < minfreq) then minfreq := freqy[j];
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end;
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flength := winwidth - (xaxislong + 150);
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for j := 1 to 51 do
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begin
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ypos := yaxislong - (j * yspacing);
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frange := maxfreq - minfreq;
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prop := (freqy[j] - minfreq) / frange;
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xpos1 := round(xoffset - 50 - (prop * flength));
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xpos2 := xoffset - 50;
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Image1.Canvas.MoveTo(xpos1,ypos);
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Image1.Canvas.LineTo(xpos2,ypos);
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end;
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Image1.Canvas.MoveTo(xoffset - 50,yaxislong);
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Image1.Canvas.LineTo(xoffset - 50,0);
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Image1.Canvas.TextOut(0,0,'Y DISTRIBUTION');
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end;
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initialization
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{$I corsimunit.lrs}
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end.
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