椭圆的拟合优度用什么指标评价啊。

我用如下的程序进行了椭圆拟合，如何评价其拟合效果啊？在网上查的用R^2，这个R^2事如何计算的呢？x=【-0.067624357，-0.003359844，0.063037813，0.089413159，0.059020652，-0.008843696，-0.071093237，-0.088206129

-0.049317504，0.020882494，0.077824328，0.085355985，0.038695664，-0.032532291，-0.083105699，-0.080915821，-0.027352997

0.043576072，0.086838968，0.074968348，0.015500796，-0.053808114-0.088954591】

y=【0.268839461 ，1.714580918，2.071745728，1.113572199，-0.551601318，-1.866566626，-1.996460517，-0.858814177，0.824087886，1.98378173，1.883985025，0.588058071，-1.081223256，-2.064042734，-1.736414456，-0.306347556，1.318217482

2.105854527，1.556497772，0.018930366，-1.530655811，-2.108438235，-1.347586479】

XY=[x,y];

F=@(p,XY)p(1)*XY(:,1).^2+p(2)*XY(:,1).*XY(:,2)+p(3)*XY(:,2).^2+p(4)*XY(:,1)+p(5)*XY (:,2)+p(6);%椭圆一般方程

p0=[1 1 1 1 1 1];

p=nlinfit(XY, zeros(size(XY,1),1), F, p0);

plot(XY(:,1), XY(:,2), 'ro');

hold on;

xmin=min(XY(:, 1));

xmax=max(XY(:, 1));

ymin=min(XY(:, 2));

ymax=max(XY(:, 2));

ezplot(@(x,y)F(p,[x,y]), [-1+xmin,1+xmax,-1+ymin,1+ymax]);

Answer 1

[xanolep]

clear,clc

x=[...];%xdata

y=[...];%ydata

fx1=@(b,x)b(1)*x+sqrt(b(2)+b(3)*x.^2);

fx2=@(b,x)b(1)*x-sqrt(b(2)+b(3)*x.^2);

b=[13.05887549, 3.096538149, -386.9576467];

y1=fx1(b,x);y2=fx2(b,x);

n=length(y);

for i=1:n

if abs(y(i)-y2(i))<=abs(y(i)-y1(i))

y1(i)=y2(i);

end

end

SSy=var(y)*(n-1),%total sum of squares

RSS=(y-y1)'*(y-y1),%residual sum of squares

Rsquare=(SSy-RSS)/SSy; %R-square

vpa(Rsquare,10)

MSe=RSS/(n-3-1),%

RMSe=sqrt(MSe)

figure(1),clf

plot(x,y,'go','markersize',10,'markerfacecolor','k')

hold on

x1=linspace(min(x)-.001,max(x)+.001,350);

y1=fx1(b,x1);y2=fx2(b,x1);

plot(x1,y1,'r-','linewidth',3)

plot(x1,y2,'r-','linewidth',3)

axis tight