Trying to find the equation of a cubic

[zebrasauce]

1. Find an equation that best fits the data?
Data
2 16.40
3 15.70
4 15.30
5 15.20
6 15.21
7 15.40
8 15.80
9 16.30
10 16.80
11 17.50
12 18.18
13 18.70
14 19.36
15 19.88
16 20.40
17 20.85
18 21.22
19 21.60
20 21.65

I have narrowed it down that it is most likely a cubic, because it seems to make sense.

I tried to use a matrix to solve this equation but found that it gave me a quartic, that did not match the data at all any help would be appreciated, is there a formula on how to solve cubics?

 

[HallsofIvy]

If you mean "find the least squares best fit cubic", you would want to write, in general, $y= ax^3+ bx^2+ cx+ d$ and then find a, b, c, d to minimize $\sum (y_i- (ax_i^3+ bx_i^2+ cx_i+ d$

 

[trigun0x2]

Have you tried simply using Finite differences?

 

[zebrasauce]

not really sure how i would use it, but ill try to

 

[war485]

I did a regression by least squares and it seems to almost perfectly fit a cubic.
a = -0.00407
b= 0.15356
c=-1.2757
d=18.27288
(approximate values)
where it is in the form y = ax^3 + bx^2 + cx + d
normally you would use a computer package like MatLab or a programmable calculator to do these. I don't recommend doing this by hand, it's very long.