Write an equation based on data

  • Thread starter musicgold
  • Start date
  • #1
275
9
Hi,

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?

Thanks.
 

Answers and Replies

  • #2
member 392791
put it on a graph and see what you get using excel
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
961
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]
 
  • #4
28
1
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.
 
  • #5
6
0
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
 

Related Threads on Write an equation based on data

Replies
4
Views
1K
Replies
19
Views
720
  • Last Post
Replies
1
Views
1K
Replies
2
Views
646
Replies
28
Views
5K
Replies
4
Views
5K
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
5
Views
15K
Replies
8
Views
2K
Top