Fit a curve to a nonlinear 1D data

Hello,

I have a monthly rainfall data for a year and it is quadratic with months. I want to get the approximate equation it follows. I tried Excel and other options and the results are also okay but I was thinking if MATLAB could give a more precise equation for me. After that, I will use that equation for another variable. Below is shown the monthly data. I just want to fit a curve to it and get the equation for my further use. Thank you very much.

18.92, 21.6, 27.4, 43.07, 85.66, 230.12, 347.02, 289.74, 197.32, 95.32, 39.5, 19

Answer 1

[Sindar]

x=1:12;
y=[18.92, 21.6, 27.4, 43.07, 85.66, 230.12, 347.02, 289.74, 197.32, 95.32, 39.5, 19];
% fit to a quadratic (degree 2) polynomial
p = polyfit(x,y,2);

[Abhishek Singh]

Thank you. I can get the co-efficients from p. Is there also a way with this that I can plot the points and also overlay my fit to see the curve fit?

[Sindar]

% half-month steps
x1 = linspace(0,12,25);
% evaluate at these points
y1 = polyval(p,x1);
figure
% plot original data with stars
plot(x,y,'*')
% add fitted data as lines
hold on
plot(x1,y1)
hold off

[Abhishek Singh]

@Sindar, thank you for commenting and answering. I know that I have mentioned it is quadratic but from the fit graph it looks like more of a polynomial of higher order. So I tried polyfit(x,y,6) and got the values of p. Would you advise any other function than polyfit() to give more precise results with lesser co-efficients in p?

[Sindar]

what do you mean by "lesser co-efficients in p"?

Also, with only 12 data points, I'd be wary of fitting with high-order polynomials (too many parameters, likely to overfit and result in spikes between sampled points)