I'm trying to figure out a general mathematical model for the following dataset;
(Time of Day, No. of Events)
(1 , 1442)
(2 , 275)
(3 , 0)
(4 , 419)
(5 , 2324)
(6 , 5769)
(7 , 8481)
(8 , 16700)
(9 , 18834)
(10 , 16101)
(11 , 8723)
(12 , 6528)
(13 , 10508)
(14 , 7320)
(15 , 10236)
(16 , 12686)
(17 , 10327)
(18 , 14210)
(19 , 11571)
(20 , 10910)
(21 , 3980)
(22 , 6274)
(23 , 3244)
(24 , 1010)
Subsets, are actually events occurring in different times of the day. All events are random. The events are dependent on the Time of day.
Take the data in pairs as $x$ and $y$ co-ordinates of points in the plane. So the given numerical data is a set of points $(x_1,y_1), (x_2,y_2),\ldots, (x_n,y_n)$ . You know given two points there is a line passing through them Line is given by a degree 1 equation, in $x$, i.e., $y=mx+c$. In general given $n$ points it can be obtained as $y=f(x)$ for a polynomial $f$ of degree $n-1$ (or less). See Lagrange Interpolation formula. See, e.g., https://en.wikipedia.org/wiki/Lagrange_polynomial