MATLAB: Which is the best degree of the polynomial

curve fittingpolynomial

I have to find an equation that models the velocity with time with the data given. I believe the fourth degree is the ideal one. Can someone confirm that please? Also, is the basic fitting and the polyfit function the same thing? The data is
T = table([0;10;15;20;32;59;62;125],[0;56.40;97.23;136.25;226.16;403.86;440.44;1265.23]);
T.Properties.VariableNames = {'Time' 'Velocity'};
v=T.Velocity;
t=T.Time;

Best Answer

I think orders 2 and 3 fit better.
T = table([0;10;15;20;32;59;62;125],[0;56.40;97.23;136.25;226.16;403.86;440.44;1265.23]);
T.Properties.VariableNames = {'Time' 'Velocity'}
v=T.Velocity;
t=T.Time;
plot(t, v, 'b*-', 'LineWidth', 3, 'MarkerSize', 18);
grid on;
tFit = linspace(min(t), max(t), 500);
hold on;
for order = 1 : 4
coefficients = polyfit(t, v, order);
vFit = polyval(coefficients, tFit);
plot(tFit, vFit, '-', 'LineWidth', 1);
end
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
You don't want to do over fitting. It can lead to really bad values in between the training points. Look how much the 4th order curve varies from "reasonable" between 90 and 110.