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I What is the function of this graph?

  1. Sep 21, 2016 #1
    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:

    Screen_Shot_2016_09_22_at_4_19_41_AM.png


    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. jcsd
  3. Sep 21, 2016 #2

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    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 )
     
  4. Sep 22, 2016 #3

    mfb

    User Avatar
    2016 Award

    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.
     
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