Science

Solve for a,b,c and d

This is a third order Polynomial Fit with the equation x = a*y^3 + b*y^2 + c*y + d. Can anyone improve on my estimates; a is 0.003596522, b is -0.8503, c is 66 and d is -1580? Here are the co-ordinates. Details of any sources used would be appreciated.
(116.3165114, 71.36645962)
(113.6052632, 74.42002461)
(108.173888, 71.76086401)
(106.0930425, 69.06894376)
(105.9976989, 66.16615532)
(109.9961508, 61.64905768)
(111.3208562, 59.59447497)
(113.6052632, 57.57997539)
(111.7986482, 55.0033795)
(107.6971184, 51.97308414)
(106.8300078, 52.44014129)
(103.7731156, 55.31507487)
(103.9561187, 56.81582202)

AG Fanclub Tue 24/06/08 14:14

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fo3nix
Wed 25/06/08
21:04

Assuming your data is of the form (x, y)

I get the following using Mathematica:

y = -54353.3 + 1495.3 x - 13.6926 x^2 + 0.0417825 x^3

Using the function Fit[data, {1, x, x^2, x^3}, x], on the data

data = {{116.3165114, 71.36645962}, {113.6052632,
74.42002461}, {108.173888, 71.76086401}, {106.0930425,
69.06894376}, {105.9976989, 66.16615532}, {109.9961508,
61.64905768}, {111.3208562, 59.59447497}, {113.6052632,
57.57997539}, {111.7986482, 55.0033795}, {107.6971184,
51.97308414}, {106.8300078, 52.44014129}, {103.7731156,
55.31507487}, {103.9561187, 56.81582202}};

AG Fanclub
Thurs 26/06/08
10:07

Question Author

Thanks for that.
If you enjoy anwering questions, you may care to sign up for Yahoo Answers, where I can be found under the handle P.W.
I would be interested in hearing from you by email, which can be done from that site.

AG Fanclub
Thurs 26/06/08
13:53

Question Author

I plotted those coefficients using Excel and (unless I'm mistaken), they mirror the above S shaped co-ordinates to create a "figure of 8" Leminiscate. Interesting!
The object of the exercise is to identify shapes in data and I have set a Floor of 1 in Excel to help me match up actual values with calculated ones. Unfortunately, using this Floor means that only one of the calculated values is a hit. I wonder if there is any way of improving on this?

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