program Kramer;
uses CRT;
const
n=25;
type
TArrayXY = array[1..2,1..n] of real;
TArray = array[1..n] of real;
var
SumX,SumY,SumX2,SumXY,SumX3,SumX4,SumX2Y,SumLnY,SumXLnY: real;
OPRlin,OPRkvadr,OPRa1,OPRa2,OPRa3:real;
a1lin,a2lin,a1kvadr,a2kvadr,a3kvadr,a1exp,a2exp,cexp:real;
Xsr,Ysr,S1,S2,S3,Slin,Skvadr,Sexp:real;
Kkor,KdetLin,KdetKvadr,KdetExp:real;
i:byte;
const
ArrayXY:TArrayXY=((12.85,12.32,11.43,10.59,10.21,9.65,9.63,9.22,8.44,8.07,7.74,7.32,7.08,6.87,5.23,5.02,4.65,4.53,3.24,2.55
,1.86,1.76,1.11,0.99,0.72) , (154.77
,145.59,108.37,100.76,98.32,81.43,80.97,79.04,61.76,60.54,55.86,47.63,48.03,36.85,25.65,24.98,22.87,20.32,9.06,6.23,3.91,3.22
,1.22,1.10,0.53));
begin
ClrScr;
SumX:=0.0;
SumY:=0.0;
SumXY:=0.0;
SumX2:=0.0;
SumX3:=0.0;
SumX4:=0.0;
SumX2Y:=0.0;
SumLnY:=0.0;
SumXLnY:=0.0;
{ Вычисление сумм x, y, x*y, x^2, x^3, x^4, (x^2)*y, Ln(y), x*Ln(y) }
for i:=1 to n do
begin
SumX:=SumX+ArrayXY[1,i];
SumY:=SumY+ArrayXY[2,i];
SumXY:=SumXY+ArrayXY[1,i]*ArrayXY[2,i];
SumX2:=SumX2+sqr(ArrayXY[1,i]);
SumX3:=SumX3+ArrayXY[1,i]*ArrayXY[1,i]*ArrayXY[1,i];
SumX4:=SumX4+sqr(ArrayXY[1,i])*sqr(ArrayXY[1,i]);
SumX2Y:=SumX2Y+sqr(ArrayXY[1,i])*ArrayXY[2,i];
SumLnY:=SumLnY+ln(ArrayXY[2,i]);
SumXLnY:=SumXLnY+ArrayXY[1,i]*ln(ArrayXY[2,i])
end;
{ Вычисление коэффициентов }
OPRlin:=0.0;
a1lin:=0.0;
a2lin:=0.0;
a1kvadr:=0.0;
OPRkvadr:=0.0;
a2kvadr:=0.0;
a2kvadr:=0.0;
a1exp:=0.0;
a2exp:=0.0;
OPRlin:=n*SumX2-SumX*SumX;
a1lin:=(SumX2*SumY-SumX*SumXY)/OPRlin;
a2lin:=(n*SumXY-SumX*SumY)/OPRlin;
OPRkvadr:=n*SumX2*SumX4+SumX*SumX3*SumX2+SumX2*SumX*SumX3- SumX2*SumX2*SumX2-n*SumX3*SumX3-SumX*SumX*SumX4;
a1kvadr:=(SumY*SumX2*SumX4+SumX*SumX2Y*SumX3+SumX2*SumXY*SumX3-
SumX2*SumX2*SumX2Y-SumY*SumX3*SumX3-SumX*SumXY*SumX4)/OPRkvadr;
a2kvadr:=(n*SumXY*SumX4+SumY*SumX3*SumX2+SumX2*SumX*SumX2Y-SumX2*SumX2*SumXY-n*SumX3*SumX2Y-SumY*SumX*SumX4)/OPRkvadr;
a3kvadr:=(n*SumX2*SumX2Y+SumX*SumXY*SumX2+SumY*SumX*SumX3-SumY*SumX2*SumX2-n*SumXY*SumX3-SumX*SumX*SumX2Y)/OPrkvadr;
a2exp:=(n*SumXLnY-SumX*SumLnY)/OPRlin;
cexp:=(SumX2*SumLnY-SumX*SumXLnY)/OPRlin;
a1exp:=exp(cexp);
{ Вычисление средних арифметических x и y }
Xsr:=SumX/n;
Ysr:=SumY/n;
S1:=0.0;
S2:=0.0;
S3:=0.0;
Slin:=0.0;
Skvadr:=0.0;
Sexp:=0.0;
Kkor:=0.0;
KdetLin:=0.0;
KdetKvadr:=0.0;
KdetExp:=0.0;
for i:=1 to n do
begin
S1:=S1+(ArrayXY[1,i]-Xsr)*(ArrayXY[2,i]-Ysr);
S2:=S2+sqr(ArrayXY[1,i]-Xsr);
S3:=S3+sqr(ArrayXY[2,i]-Ysr);
Slin:=Slin+sqr(a1lin+a2lin*ArrayXY[1,i]-ArrayXY[2,i]);
Skvadr:=Skvadr+sqr(a1kvadr+a2kvadr*ArrayXY[1,i]+a3kvadr*ArrayXY[1,i]*ArrayXY[1,i]-ArrayXY[2,i]);
Sexp:=Sexp+sqr(a1exp*exp(a2exp*ArrayXY[1,i])-ArrayXY[2,i]);
end;
{ Вычисление коэффициентов корреляции и детерминированности }
Kkor:=S1/sqrt(S2*S3);
KdetLin:=1-Slin/S3;
KdetKvadr:=1-Skvadr/S3;
KdetExp:=1-Sexp/S3;
{ Вывод результатов }
WriteLn('lineynaya funkcia'); readln;
WriteLn('a1=',a1lin:8:5);
WriteLn('a2=',a2lin:8:5);
WriteLn('kvadratichnaya funkcia'); readln;
WriteLn('a1=',a1kvadr:8:5);
WriteLn('a2=',a2kvadr:8:5);
WriteLn('a3=',a3kvadr:8:5);
WriteLn('eksponencialnaya fukcia'); readln;
WriteLn('a1=',a1exp:8:5);
WriteLn('a2=',a2exp:8:5);
WriteLn('c=',cexp:8:5);
WriteLn('Xcp=',Xsr:8:5);
WriteLn('Ycp=',Ysr:8:5);
WriteLn('koefficient korrelyacii ',Kkor:8:5); readln;
WriteLn('koefficient determinirovannosti (lineynaya approksimacia) ',KdetLin:2:5); readln;
WriteLn('koefficient determinirovannosti (kvadraticheskaya approksimacia) ',KdetKvadr:2:5);readln;
WriteLn('koefficient determinirovannosti (eksponencialnaya approksimacia) ',KdetExp:2:5); readln;
end.
|
