Polyfit in case of power function

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Ede gerlderlands 2013-7-29

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https://ww2.mathworks.cn/matlabcentral/answers/83427-polyfit-in-case-of-power-function

Hi All. I have an equation of the form y=b+ a.x^(1/3)

I tried to fit a line by assuming

 m=x^(1/3);
 p=polyfit(m,y,1);
 f=polyval(p,m);
 plot(x,y,'o',x,f,'-');

but the plot isn't satisfactory. Is there any wrong with the code or is the problem with my selection of fitting equation?

Regards,

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Ede gerlderlands 2013-7-29

Thank you very much

dpb 2013-7-29

在 MATLAB Online 中打开

To get a grasp on what's going on, try the following...

plot(x,y)
b=polyfit(xp(6:end),y(6:end),1);
hold on, plot(x(6:end),polyval(b,xp(6:end)),'ro')
b=polyfit(xp(1:5),y(1:5),1);
plot(x(1:5),polyval(b,xp(1:5)),'go')

This separates the two sections of positive and negative curvature and fits the two regions separately.

As this clearly shows, x^1/3 is both too "weak" a correlation early on and of the opposite curvature later. There's simply no way you can adequately model these data w/ a single functional form of the type of a power relationship--they just don't follow that as a model.

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