# Which is the best degree of the polynomial?

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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;

Image Analyst on 22 Nov 2017
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.
Sakusan Puwanendran on 22 Nov 2017
I get a similar shape as yours for the 4th degree when using the basic fitting function on the graph figure however when I use the polyfit function I get a different function. Could you explain what I'm doing wrong? My code for polyfitting
p4 = polyfit(t,v,4) %4th DEGREE POLYNOMIAL FITTING
f4 = polyval(p4,t);
plot(t,v,t,f4)