[cotang]

First off I want to say this is a great site!

My question is, that given 2 variables (X&Y) the linearity can be found using y=mx+b. But if 3 variables are given (X&Y&Z) where X & Y affects Z, how would or what formula do you use to find the linearity of that? or could you?

Thanks.

[Donaldson Tan]

are you familar with vector equation for a line?

r = m(a b c)^T + (d e f)^T

where m is any real number, which you vary to get all the points on the line; (a b c)^T is the direction vector (similar to gradient) of the line; (d e f)^T is any point on the line.

[cotang]

Thank you for your reply.

No I'm not familiar (or remember) the vector formula. Will that work with linearity with 3 variables? I'm not sure how to implement that.

[Donaldson Tan]

it is the vector equation for a straight line (in a 3D graph)

i shall rid some of the notations to simplify 3D linear equations for you.

ignore the T which means transpose. It just mean (1 2 3) should be written vertically, not horizontally.

I write each coordinate (x,y,z) as (x y z), ie. i get rid of the commas.

r refers to the coordinate of any point on the straight line, ie. let r = (x y z)

(x y z) = m(1 2 3) + (4 5 6)

when m = 0, (x y z) = (4 5 6)
when m = 1, (x y z) = (5 7 9)

the value of m varies from negative infinity to infinity, and all points it generate lies on the same straight line. (1 2 3) is the 3D equivalent of gradient. It decides the orientation of the straight line. (1 2 3) can be adjusted to any values.

[cotang]

Ahh...yes I kinda see, but I think I might have mislead you on my question. Let me try that again.

Ok given 3 variables X,Y, and Z, how X and Y affects Z independantly, How do I determine how much X affect Z and Y affect Z if I have collected information on a three variables. So far all I manage to do is graph the information and by using Excel Linear Regression I manage to get the Y=MX+B vaules. See pic.

If you take a concentration value of x or y solution and sub it into the Y formula you can get x with is equal to the Z out come, but that takes into account of the other solution.

Example. Lets take 30% Concentration of Linear Solution Y and 10% Concentration of Linear Soltuion X  that gives about 25% of solution Z for Y and 2.3% of Solution Z for X. Now this doesn't seems right given that my gathered data doesn't seem to correlate that. Because by adding Solution X and Y you get a certain amount of Z.

Tough huh? So I guess my question is How do I find how much X affect Z and Y affect Z relating to the data gathered.

[Donaldson Tan]

I think you are looking for partial derivative. Here's a good website to make reference to: http://mathworld.wolfram.com/PartialDerivative.html