# I What is the function of this graph?

1. Sep 21, 2016

### beamthegreat

I need to create a non linear function from a list of points. I tried creating a 3rd order polynomial trendline on excel but it was a very poor fit. Can anyone give me tips/advice on how to create a function that best fits the following data?

Here's what the graph looks like:

Here are the points:

63,400
63,468
63,588
63,759
63,981
64,252
64,571
64,939
65,355
65,818
66,329
66,886
67,490
68,141
68,839
69,584
70,375
71,214
72,100
73,033
74,014
75,042
76,119
77,244
78,418
79,641
80,912
82,233
83,602
85,021
86,489
88,006
89,571
91,183
92,843
94,549
96,299
98,093
99,927
101,799
103,707
105,646
107,612
109,600
111,603
113,614
115,625
117,624
119,599
121,538
123,423
125,234
126,951
128,545
129,988
131,244
132,272
133,024
133,444
133,470
133,024
132,021
130,359
127,920
124,567
120,139
114,450
107,282
98,380
87,448
74,137
58,042
38,685
15,508

2. Sep 21, 2016

### FactChecker

For a curve like this, there are two popular options you might want to consider. One is to allow a higher degree polynomial. To fit that curve the degree might be higher than you want. Another option is to fit it in parts with a spline function. A spline of certain orders can be pieced together so that the function and derivatives of orders up to a desired order are continuous.

There is a popular statistical package, R, that has spline function capability. (see https://stat.ethz.ch/R-manual/R-devel/library/stats/html/splinefun.html )

3. Sep 22, 2016

### Staff: Mentor

13750 * (3.6 + exp(i/17.5)) * (1-i/74.3)^0.77
Where the first element in the dataset has i=1 and the last one has i=74.

Found by black magic and sacrificing a few electrons. A spline will give better results but my formula is accurate to better than 1% apart from the last few bins. I tuned the parameters manually, an automatic approach will find a better fit.