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i1  16  64  400 25  8   8
i2  1   1   1   4   3   3
i3  4   20  40  4   100 200

min 10  15  35  14  30  35
max 10  20  45  16  30  45

How can I get the function of this correlation?

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The question is not clear to me. What is the input values and output values for each function (x,y)? For example, for first function, is f1(4)=400? What does the min and max mean? – NoChance Sep 4 '12 at 10:29
the inputs are i1,ix,i3 and the output is x, that should be between min and max – user65130 Sep 4 '12 at 10:31
for example for the first row applay the function: i1-i3-2*i2 , but this does not applay for every column, I'm looking for a founction that applays for every column – user65130 Sep 4 '12 at 10:35
you could try regression of the min/max against $i1$, $i2$, $i3$. – Max Sep 4 '12 at 11:47
up vote 0 down vote accepted

If we can assume the function has the form: $f(i_1,i_2,i_3)=a\times i_1 +b\times i_1+c\times i_1$
If we had the exact value of the function at 3 different$(i_1,i_2,i_3)$ then the coefficients could be driven deterministically by solving a $3\times 3$ matrix equation.
Here we are given max and min value of a given combination so a good approach will be:

1.choose 3 equations out of 6 (20 cases)
2.solve the $3\times 3$ matrix equation once for min and once for max and derive eight(two cases for each equation) $f(i_1,i_2,i_3)$
3.check that $f(i_1,i_2,i_3)$ meets the constraints imposed by other 3 equations and chosen 3 equations( 3*2+3 = 9 in total)
If met, one possible $f(i_1,i_2,i_3)$ is found and go back to step 1
else If not met and there is a 6C3(all 20 cases are NOT checked) go back to step1
else If there is no more 6C3(all 20 cases are checked) output functions found

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