Creating a function given a set of data points-CodePudding

I am working on a function in C programming and would like to create a function based off of the given data points but I cannot seem to get something that fits this curve. See graph here:

graph

My program will primarily use this function in the 0-500°F range so it is important that this range is accurate.

Using this graph I have determined the data points to be approximately:

Temp(F), Factor

(-300, 1.57)
(-200, 1.33)
(-100, 1.16)
(0, 1.05)
(100, 0.98)
(200, 0.94)
(300, 0.915)
(400, 0.865)

I have found that y = 0.00000244x^2 -0.001x 1.05 is a close fit for the -300-100°F range but gets very bad for x>100°F values.

y = 1.6904761904745*10^-6 x^2 - 0.00109048x 1.0628 seems to be closer.

I figure that I need a cubic function to model this well, but I can't figure out what it would be. Any recommendations? I was also thinking that I could model T<200°F & T>200°F as separate functions.

EDIT I have found a set of linear piecewise functions that fit the dataset, still probably inaccurate for the 400-500°F range.

1.) y=-0.0024x   0.85 {-300< x <-200}
2.) y=-0.0017x   0.99 {-200< x <-100}
3.) y=-0.0011x   1.05 {-100< x < 0}
4.) y=-0.0007x   1.05 {0 < x <100}
5.) y=-0.0004x   1.02 {100 < x < 200}
6.) y=-0.00025x   0.99 {200 < x < 300}
7.) y=-0.0005x   1.065 {300< x < 400}
8.) y=-0.00065x   1.125 {400< x < 500} *estimated factor to be 0.8 @ 500°F*

EDIT2

I was able to model this pretty well with the help of

CodePudding user response：

Another convenient model (exponential function) :

Method of fitting from https://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales