Some statistics help

[vdg]

I have some data that has to be analized/predicted.
There are 2 numbers : 1.3 0.9 for ex.
For each of those sets(1 set=2 numbers) I have another 10 values like: 100 89 55 ..etc Those value are produced by some formulas named A B C D ..etc

I want to find ,for a given set(2 numbers), which 3(three) of the A B C D..etc, formulas would give me the highest values.

To be more explicit- here is the input
A B C D .....
1.2 2.3 100 89 55 123
2.3 4.3 33 44 223 4
.
.
.
..and now I want to predict/analize which of the A B C D..etc would give me the highest number if the input is 3.2 0.9

Any idea how to attack this problem?

 

[gbuskirk]

Theoretically, your problem implies a three-dimensional coordinate system problem. The 10 values are 10 functions A,B,C,D,E,F,G,H,I,J of X and Y.

Your first question can be reworded as: Given a new X and Y for which no data is known, surmise which three functions are greatest. One approach is determining three points closest to X and Y, which define a triangle in which this point lies. Then interpolate for each function, what value it would be at point X and Y. Then sort by height. It's not a simple calculation.

There may be other curve fitting approaches, which would probably be even greater complexity.

 

[CycloWizard]

As gbuskirk suggests, the first thing to do is see if you can fit A, B, C, etc... to analytical functions f(x,y) where x and y are your inputs. If you can do this, then the procedure may be programmed in a relatively straightforward manner. Just plug in the input (x,y) ordered pair in the expression for each function, then sort the outputs. If the functions are not analytic, then you could approximate them as analytic functions (again, using regression techniques), possibly in a piecewise manner, or interpolate between the known, discrete data points. The first is probably preferable unless the approximate fitting is poor. The second is probably easier to program, depending on the number of points you want to consider during interpolation. The number of data points considered will also affect which method is more accurate and computationally inexpensive.