# problem constructing an equation that connects variables

need a suggestion/advice/inputs from the mathematicians here.

I have collected data of number of instructions/sec executed by a processor every second, number of loads/stores performed every second and stored the array of values in 2 files.

I also simultaneously collected data of the energy consumed every second by the entire computer and stored it in a file.

Assuming,

(eg :

 INstructions/sec   loads and stores/sec    energy consumed by computer/sec
12344                    2134124                    234
345345                   2342123                    234
324525                   4443214                    345
345324                   1432132                    234
.                          .                       132
.                          .                       321
.                          .


[A] to be an array of number of instructions executed/sec every second

[B] is the array of loads and stores/sec every second, (

[C] is the array of energy values every second, how can i find an equation connecting A, B and C ?

Should I use curve fitting ? What is the approach I should employ? Eigen vectors ? I'm a bit out of touch with Mathematics since it's been quite long.

The equation can be of any form.. Not just [A]x + [B]y =[C]

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Least squares shall be your savior. – J. M. May 1 '11 at 4:27
what does X and Y stand for? why do you need an equation of that form? – Mark May 1 '11 at 4:32
The equation can be of anyform.. I just need to build an equation that finds a relation between [A] , [B] and [C] – Sharat Chandra May 1 '11 at 5:08
@Sharat: please do not use answers to make comments. Your accounts have been merged so you should now be able to comment normally on this question. – Qiaochu Yuan May 1 '11 at 5:19
If you allow equations of "any form", there are infinitely many equations that will exactly fit the data. So you shouldn't be asking "How can I find any equation that connects these variables?" but rather, "Given this data, how should I try to find what the actual relationship is between these variables?" This is a problem in regression analysis, and it seems to me that not wanting to specify the form of the equation could introduce many subtle complications. You would probably get a better discussion at the statistical analysis site, stats.stackexchange.com – Rahul Narain May 1 '11 at 6:35
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