How to get a polynomial fit to a set of data without using "fit" function?

Here is my matlab code for trying to get a fourth degree polynomial fit to a graph. The first code I attached is a code I wrote for a second degree polynomial code that does work, but I'm not sure why the fourth-degree one doesn't work. The second code is my attempt at the fourth degree one.

[Mikhail]

Why do you avoid fit function? If because of toolbox required, try to use polyfit

Answer 1

[Star Strider]

You’re calculating your ‘polynomialerror’ incorrectly. You start by modeling your system as: Y = B*V, and you correctly calculate your estimated ‘V2’ parameter vector as: V2 = B\Y. You have to calculate the estimated fit as: Yfit = B*V2, and compare Y'-Yfit to calculate your error. Otherwise, you got everything correct, and your fit looks good when plotted:

X=[1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8];
Y=[0.5 0.61 0.66 0.57 0.45 0.028 -0.16 -0.49 -0.45 -0.5 -0.32 -0.017 0.36 0.59 0.69];

B=[X'.^4,X'.^3,X'.^2,X',ones(15,1)];
V2=B\Y';
Yfit = B*V2;
polynomialerror=norm(Y'-Yfit)

figure(1)
plot(X,Y,'*r')
hold on
plot(X, Yfit)
hold off
grid

[Hannah]

That looks great! Thanks for explaining it so well.

[Star Strider]

My pleasure!