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

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Petch Anuwutthinawin on 20 Jul 2021
Commented: John D'Errico on 20 Jul 2021
%for a certain file, the first column is the independent variable and
%second is the dependent variable.
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?

Torsten on 20 Jul 2021
Replace x by
x = [h.^2 h ones(length(h),1)]
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John D'Errico on 20 Jul 2021
@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.

Simon Chan on 20 Jul 2021