Using the \ operator to fit a parabolic curve to a data set.

Question

Petch Anuwutthinawin 2021-7-20

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https://ww2.mathworks.cn/matlabcentral/answers/882353-using-the-operator-to-fit-a-parabolic-curve-to-a-data-set

评论： John D'Errico 2021-7-20

%for a certain file, the first column is the independent variable and
%second is the dependent variable.
C=xlsread('super.xlsx');
h=C([2:13],1); 
x=[h ones(length(h),1)] %I use a column of ones in order to simulate a constant secondary dependent variable. 
y=C([2:13],2); % the dependent variable
V=x\y %This command only gives me one value, that is just a linear fit. How do I make this use a parabolic fit instead?

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Answer 1

Torsten 2021-7-20

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https://ww2.mathworks.cn/matlabcentral/answers/882353-using-the-operator-to-fit-a-parabolic-curve-to-a-data-set#answer_750478

Replace x by

x = [h.^2 h ones(length(h),1)]

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Tesfaye Girma 2021-7-20

yhat = (M'*M)\(M'*x);

John D'Errico 2021-7-20

在 MATLAB Online 中打开

@Tesfaye Girma - NO. Don't tell people to use an inferior method to estimate a linear regression model.

In MATLAB, it is correct to use this:

coef = M\x;

Use of the normal equations (what you showed) will cause significantly increased sensitivity to poorly conditioned problems. That scheme will completely fail to work on many solvable problems.

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