Trying to find the equation of a cubic

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    Cubic
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Homework Help Overview

The discussion revolves around finding a cubic equation that best fits a given set of data points. The original poster suggests that a cubic model is appropriate based on their observations of the data trends.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the method of least squares for fitting a cubic equation, with one suggesting the general form of the cubic equation. Others mention alternative methods like finite differences and express uncertainty about their application.

Discussion Status

There are various approaches being explored, including regression analysis and the use of computational tools. Some participants have shared specific coefficients from their regression attempts, while others are still considering how to apply different methods.

Contextual Notes

Participants note the complexity of solving cubic equations by hand and the potential for confusion when using matrices, as one participant experienced a quartic result instead. There is also mention of using software tools for regression analysis.

zebrasauce
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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?
 
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If you mean "find the least squares best fit cubic", you would want to write, in general, [itex]y= ax^3+ bx^2+ cx+ d[/itex] and then find a, b, c, d to minimize [itex]\sum (y_i- (ax_i^3+ bx_i^2+ cx_i+ d[/itex]
 
Have you tried simply using Finite differences?
 
not really sure how i would use it, but ill try to
 
Last edited:
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.