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

%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?

Answer 1

[Torsten]

Replace x by

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

[Tesfaye Girma]

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

[John D'Errico]

@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.

Answer 2

[Simon Chan]

use function polyfit with n = 2

p = polyfit(x,y,n)

[p,S] = polyfit(x,y,n)

[p,S,mu] = polyfit(x,y,n)