Working with three variables (1 Viewer)

[iversion]

If I have 2 variables, A and B (A+B = 1), and i wanted to see the effect of varying these two on a quantity Q then i could just do an experiment where i go:

A: B
1: 0
0.8: 0.2
0.6: 0.4
0.4: 0.6
0.2: 0.8
0: 1

and measure Q for each ratio (and choose the ratio which gives the best Q).

But how do i go about it when i have 3 variables, A, B and C, and want to set up an experiment that will find the optimum ratio of A:B:C which gives an optimum value of Q?

How do i make sure i don't miss any ratios of A:B:C?


Thanks for any help

 

[Iruka]

And exactly how is Q determined?

 

[iversion]

experimentally, by performing some tests.


SHould i see what the optimum ratio of A:B is (ie find the ratio of A:B for which Q is optimised)
and then take that blend of A & B and do the following:


A&B : C
1: 0
0.8: 0.2
0.6: 0.4
0.4: 0.6
0.2: 0.8
0: 1

and take the optimum of that as being the optimum A:B:C ratio?

 

[Iruka]

Yes, but how is Q related to A, B and C?

For instance, is Q=A*B*C? Q=A+B+C? Q =A^2+B^2+C^2, etc?

 

[iversion]

its unknown.
which is why experiments are needed to determine the relationship.if the relatinoship Q = f (A,B,C) was known, we wouldnt need to be doing any experiments..


but to establish the relationship, first we need to set up the experiment itself.
this is where i need to know how to set up an experiment when there are three variables that need to be considered. like three independent variables, how do i set up the experiment?

 

[Affinity]

You need to know something about Q to answer that.. not the formula, but atleast some properties of Q..

is it smooth for example...

If you know nothing about Q then you can't deduce anything... even in the 2 variable case, because you could try
0.1,0.9;0.2;0.8 ...
but Q can have a spike at (0.55555,0.44445) and you will miss that

 

[iversion]

You need to know something about Q to answer that.. not the formula, but atleast some properties of Q..

is it smooth for example...

If you know nothing about Q then you can't deduce anything... even in the 2 variable case, because you could try
0.1,0.9;0.2;0.8 ...
but Q can have a spike at (0.55555,0.44445) and you will miss that

yeap its smooth. some sort of polynomial

 

[Affinity]

experimentally, by performing some tests.


SHould i see what the optimum ratio of A:B is (ie find the ratio of A:B for which Q is optimised)
and then take that blend of A & B and do the following:


A&B : C
1: 0
0.8: 0.2
0.6: 0.4
0.4: 0.6
0.2: 0.8
0: 1

and take the optimum of that as being the optimum A:B:C ratio?

This does not work unless you know more about Q. You are essentially assuming that Q = f(a,b,c) = f(a,b,1-a-b) = g(a+b)
for some function g. In many cases this is false so you are forced to test Q for (a,b) ranging over a grid of points in a triangle in [0,1]x[0,1] (a+b<1)

So again you are back to the question... what else do you know about Q