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Polyfit minus one term

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Hi, and happy new year.
I need a 3rd order polynomiial approximation for the file Data001 in attached.
I can use polyfit but I need a polinomium without the term x^2.
My polinomium must be:
x^3+x^1+x^0.
How can I do that?

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Accepted Answer

Star Strider
Star Strider on 1 Jan 2020
Use the mldivide,\ function with a specific design matrix (since this is a linear problem):
D = load('Data001.mat');
x = D.Data001(:,1);
y = D.Data001(:,2);
DesignMatrix = @(x) [x.^3 x ones(size(x))];
B = DesignMatrix(x) \ y;
xv = linspace(min(x), max(x), 1000);
yv = DesignMatrix(xv(:)) * B;
figure
plot(x, y, '.')
hold on
plot(xv(:), yv(:), '-r')
hold off
grid
xlabel('x')
ylabel('y')
legend('Data001', 'Regression Fit')
producing:
The ‘B’ vector are the respective regression coefficients, so that y(x) = B(1)*x^3 + B(2)*x + B(3).

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Paul Rogers
Paul Rogers on 1 Jan 2020
oh my god, thank you. One thing I asked wrong,
I need x^3+x^2+x^0. The one I don't need is the therm x^1
Star Strider
Star Strider on 1 Jan 2020
My pleasure!
I was confused by your original Question, since you only left out ‘x^2’.
To leave out ‘x^1’, change ‘DesignMatrix’ to:
DesignMatrix = @(x) [x.^3 x.^2 ones(size(x))];
Also, your vectors are column vectors here, and this will only work with column vectors. To enforce that if you have row vectors, the ‘B’ calculation becomes:
B = DesignMatrix(x(:)) \ y(:);
since the ‘(:)’ will force ‘x’ and ‘y’ to become column vectors.
With that change, the ‘B’ vector are the respective regression coefficients, so that y(x) = B(1)*x^3 + B(2)*x^2 + B(3).
Star Strider
Star Strider on 1 Jan 2020
If my Answer helped you solve your problem, please Accept it!

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More Answers (1)

dpb
dpb on 1 Jan 2020
Without toolbox, use backslash operator, \
X=[x.^[3 2 1 0]]; X(:,2)=0; % design matrix straight calculation
b=X\y; % solve for coefficients
If have Stat or Curve Fitting TB, use one of the linear model fitting routines with custom model.

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