write an equation based on data

by musicgold
Tags: based, data, equation, write
musicgold is offline
Oct23-13, 08:58 PM
P: 177

I am trying to understand what is the best way to solve problems like the one below. I have a few data points and I need to which function best describes that data.

(x, y) = (-3, -32) (-2, 16) (-1, 8) (0,4) (1,2) (2, 1)

note that the y parameter in the first data point is -32 and not 32.

Is there a process to solve such problems or do I have to guess the function?

Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
Woopydalan is offline
Oct23-13, 11:56 PM
P: 746
put it on a graph and see what you get using excel
HallsofIvy is offline
Oct24-13, 07:45 AM
Sci Advisor
PF Gold
P: 38,877
There are, of course, an infinite number of functions whose graphs go through those points. The unique fifth degree polynomial that fits is the Lagrange polynomial:
[tex]-32\frac{(x+ 2)(x+ 1)(x)(x- 1)(x- 2)}{(-3+2)(-3+ 1)(-3)(-3- 1)(-3-2)}+ 16\frac{(x+ 3)(x+ 1)(x)(x- 1)(x- 2)}{(-2+3)(-2+ 1)(-2)(-2- 1)(-2-2)}+ 8\frac{(x+ 3)(x+ 2)(x)(x- 1)(x- 2)}{(-1+3)(-1+ 2)(-3)(-1-1)(-1-2)}+ 4\frac{(x+ 3)(x+ 2)(x+1)(x- 1)(x- 2)}{(0+3)(0+2)(-0+ 1)(0- 1)(0-2)}+ 2\frac{(x+3)(x+ 2)(x+ 1)(x)(x- 2)}{(1+ 3)(1+2)(1+ 1)(1)(1-2)}+ \frac{(x+ 3)(x+ 2)(x+ 1)(x)(x- 1)}{(1+ 3)(1+2)(-3+ 1)(-3)(-3-2)}[/tex]

AlexVGheo is offline
Oct25-13, 03:13 PM
P: 28

write an equation based on data

There are several methods for example newton's forward difference interpolation which though quite difficult to do and limited in the fact that you have to have a constant difference between the terms it is very effective, because if the data points are from an arithmetic series it will give you an expression of the series. Above is an example of Lagrange's method which is far easier to do, less limited as the data points can be anything and returns a polynomial that works.
alzabroo is offline
Oct26-13, 10:16 PM
P: 6
1. As you've emphasized that the first data is in fact not an error it may not be helpful to point out that the last five data points are in the function: y = (2^(2-x)) , but if a piecewise function is an option than it's worth a thought.
2. Otherwise you can use excel as Woopydalan said. However adding a linear trend line will do you no good. If I remember correctly there is an option for fitting a polynomial of higher degrees. It may go up to a sixth degree polynomial.
3. The Lagrange polynomial method that HallsofIvy posted will definitely work.......so actually forget what I said and just copy and paste that into wolfram alpha

Register to reply

Related Discussions
C++ compiler to write not-very-complex DOS/text-based programmes Programming & Computer Science 20
Write an exponential equation from this data (data table included) Precalculus Mathematics Homework 2
Good Ol' Seagulls and Clams - Creating an equation based on data Precalculus Mathematics Homework 1
C++ read/write data help Engineering, Comp Sci, & Technology Homework 1
write data on any surface ??? Computing & Technology 13