ChatterBank1 min ago
Solve for a,b,c and d
3 Answers
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)
(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)
Answers
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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}};
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}};
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?
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?