matlab中的多项式拟合统计量

Question

我正在使用mathowrks示例计算多项式拟合：

load census
figure
plot(cdate,pop,'ro')
corrcoef(cdate,pop)

figure
% Calculate fit parameters
[p,ErrorEst] = polyfit(cdate,pop,2);
% Evaluate the fit
pop_fit = polyval(p,cdate,ErrorEst);
% Plot the data and the fit
plot(cdate,pop_fit,'-',cdate,pop,'+');
% Annotate the plot
legend('Polynomial Model','Data','Location','NorthWest');
xlabel('Census Year');
ylabel('Population (millions)');

如何找到这种拟合的相关性？通过简单的线性关系，我可以使用corrcoef来计算拟合，但在mathworks网站上他们只提到“他的下图显示二次多项式拟合提供了对数据的良好近似”，但不进入任何统计。

有人可以推荐一种方法吗？

http://www.mathworks.co.uk/help/matlab/data_analysis/programmatic-fitting.html

Answer 1

您可以使用以下内容：

ft_ = fittype('poly2');
[cf,gf,o] = fit(cdate,pop,ft_)

当我这样做时，我的结果是：

cf = 

     Linear model Poly2:
     cf(x) = p1*x^2 + p2*x + p3
     Coefficients (with 95% confidence bounds):
       p1 =    0.006541  (0.006124, 0.006958)
       p2 =      -23.51  (-25.09, -21.93)
       p3 =  2.113e+004  (1.964e+004, 2.262e+004)

gf = 

           sse: 159.029299176792
       rsquare: 0.998712965772009
           dfe: 18
    adjrsquare: 0.998569961968899
          rmse: 2.97236624011533


o = 

        numobs: 21
      numparam: 3
     residuals: [21x1 double]
      Jacobian: [21x3 double]
      exitflag: 1
     algorithm: 'QR factorization and solve'
    iterations: 1