8. (B) Program for Polynomial Regression.

8. (B) Program for Polynomial Regression.

	x=[0,1,2,3,4,5]; y=[2.1,7.7,13.6,27.2,40.9,61.1];
	sumy=0;
	sumx=0;
	m=2;
	n=6;
	s=0;
	xsqsum=0;
	xcsum=0;
	x4sum=0;
	xysum=0;
	x2ysum=0;
	rsum=0;
	usum=0;
	for i=1:6
	sumy=sumy+y(i);
	sumx=sumx+x(i);
	r(i)=(y(i)-s/n)^2;
	xsqsum=xsqsum+x(i)^2;
	xcsum=xcsum+x(i)^3;
	x4sum=x4sum+x(i)^4;
	xysum=xysum+x(i)*y(i);
	x2ysum=x2ysum+y(i)*x(i)^2;
	rsum=r(i)+rsum;
	end
	disp(sumy,"sum y=")
	disp(sumx,"sum x")
	xavg=sumx/n;
	yavg=sumy/n;
	disp(xavg,"xavg=")
	disp(yavg,"yavg=")
	disp(xsqsum,"sum x^2=")
	disp(xcsum,"sum x^3=")
	disp(x4sum,"sum x^4=")
	disp(xysum,"sum x*y=")
	disp(x2ysum,"sum x^2*y=")
	J=[n,sumx,xsqsum;sumx,xsqsum,xcsum;xsqsum,xcsum,x4sum];
	I=[sumy;xysum;x2ysum];
	X=inv(J)*I;
	a0=det(X(1,1));
	a1=det(X(2,1));
	a2=det(X(3,1));
	for i=1:6
	u(i)=(y(i)-a0-a1*x(i)-a2*x(i)^2)^2;
	usum=usum+u(i);
	end
	disp(r,"(yi-yavg)^2=")
	disp(u,"(yi-a0-a1*x-a2*x^2)^2=")
	plot(x,y);
	xtitle('x vs y','x','y');
	syx=(usum/(n-3))^0.5;
	disp(syx,"The standard error of the estimate based on regression polynomial=")
	R2=(rsum-usum)/(rsum);
	disp("%",R2*100,"Percentage of original uncertainty that has been explained by the model=")