Why does polyfit/polyval not work for fitting a 2nd degree polynomial to my dataset?

Question

Austin M. Weber 2021-12-19

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https://ww2.mathworks.cn/matlabcentral/answers/1614415-why-does-polyfit-polyval-not-work-for-fitting-a-2nd-degree-polynomial-to-my-dataset

评论： Star Strider 2021-12-19

data.mat

I am trying a fit a 2nd degree polynomial to my data, but it is not working the way I expected it to. What might I be doing wrong, and how can I fix this? Here is what I have:

load data.mat

% ^ Contains a variable, p, which is 57x2 double. I want to plot the first

% column as my x-axis and the second column as my y-axis

figure

plot(p(:,1),p(:,2),'k*') % plot each point as a black asterisk

% Fit a 2nd-degree polynomial to the figure

c = polyfit(p(:,1),p(:,2),2);

yFit = polyval(c,p(:,1));

hold on

plot(p(:,1),yFit,'m-') % plot polynomial fit as a magenta line

hold off

Shouldn't the polynomial line be a singular, smooth line?

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Answer 1

Star Strider 2021-12-19

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https://ww2.mathworks.cn/matlabcentral/answers/1614415-why-does-polyfit-polyval-not-work-for-fitting-a-2nd-degree-polynomial-to-my-dataset#answer_858585

在 MATLAB Online 中打开

Nothing is wrong. The data simply need to be sorted in order to plot the regression equaiton correctly.

Try this first —

LD = load('data.mat');
p = LD.p;
ps = sortrows(p,1);
figure
plot(ps(:,1),ps(:,2),'k*') % plot each point as a black asterisk
% Fit a 2nd-degree polynomial to the figure
c = polyfit(ps(:,1),ps(:,2),2);
yFit = polyval(c,ps(:,1));
hold on
    plot(ps(:,1),yFit,'m-') % plot polynomial fit as a magenta line
hold off

To get a slightly smoother regression curve plot —

ps1 = linspace(min(ps(:,1)), max(ps(:,1)), 150);
figure
plot(ps(:,1),ps(:,2),'k*') % plot each point as a black asterisk
% Fit a 2nd-degree polynomial to the figure
c = polyfit(ps(:,1),ps(:,2),2);
yFit = polyval(c,ps1);
hold on
plot(ps1,yFit,'m-') % plot polynomial fit as a magenta line
hold off

.

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Austin M. Weber 2021-12-19

Thank you, both methods work perfectly. I was not aware that polyval does not automatically sort the x values.

Star Strider 2021-12-19

As always, my pleasure!

The sort order is irrelevant to polyfit and other parameter estimation routines, however very important to evaluating the estimated parameters and plotting the resulting curve.

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