Calculate Ratio from Data: X/Y Value Comparison

[the_dialogue]

I have data arranged like this:

-----------Combo1---------Combo2
X-----------18-----------------15
Y-----------0------------------3
Value------5.44---------------7.63

So (18,0)--> 5.44 and (15,3)--> 7.63. Now different values of X and Y affect "Value". So it's two indepent variables affecting the depend variable, "Value".

I need to figure out what the exchange rate of X and Y is. In other words, i need the Ratio X=kY where k is a constant of some sort.

My first strategy was to generate 2 random pairs of values for (X,Y) that both give the same "Value". Then, i could deduce the ratio. E.g. If (10,0) and (15,10) give the same Value, then the ratio is 5X=10Y or X =2Y. But this has proven difficult because the values are difficult to generate!

How could i determine the ratio strictly from the 2 columns above (keeping the Value(s) different)?! Is this possible?!

 

[berkeman]

If x=18 and y=0, then k=infinity...

 

[the_dialogue]

If x=18 and y=0, then k=infinity...

I know. That's why there must always be a change in both X and Y.

For example, if (15,0) and (10,2) give the same Value, then the ratio is 5X = 2y. And hence, k = 2/5.

 

[quasar987]

What berkeman is saying is that the function of two variables value(X,Y)=z is not such that given a fixed value of z, the solutions {(X,Y)} are related by a proportionality relation X=kY, because we know that (18,0) is a solution of z(X,Y)=5.44, but there is no k such that 18=k0.

There is however, a k such that k18=0; it is k=0.

In general, the function that will give a relation btw X and Y of the form kX=Y when you fix z is of the form

$$z(X,Y)=c_1\frac{Y}{X}+c_2$$

You can find the values of c_1 and c_2 using the values in your table. Now just generate a 3rd set of value (X,Y,z(X,Y)). If they do not satisfy the above equation, then z(X,Y) is not of this form and givena fixed z, X and Y are not related by a simple proportionality constant. They are related by something more complex.

A simpler way still would be to verify if z(X=0,Y=anything) exists (i.e. is not infinity). If it does, then it is sufficient to conclude that z is not of the above form.