It's clear for me to count correlation and regression between two variables, e.g. X and Y. Assume, that X is a fuel consumption and Y is engine displacement. I've got a data set with 100 pairs X Y, and based on those I can calculate a correlation rate between X and Y which in this case is obvious. So I'm trying to find some dependency between X and Y and check how Y affects X.
But how about the situation when there are three variables (X, Y, Z) and I want to calculate correlation between X and (Y Z) as a group. Assume once again, that Z is a mass of vehicle and I want to check if mass of vehicle and engine displacement (Z and Y) influence on the fuel consumption X.
It's easy to everyone to notice a dependency in my ordinary example:
X may be called normal (is inside some range, expressed as number) when Y is normal and Z is normal, X is high when Y is normal and Z is high, X is very high when Y is low and Z is high, X is low when Y is low and Z is normal
and so on...
So, I've got a data set again, this time with 3 columns: X, Y and Z and I want to find (or not) the relationship between X and YZ.
I know that I can express Y and Z as a one number - some average, but then it makes no sense because of the fact that the extreme values will give the same average.
Look that there are only 3 variables here and the dependency is noticeable for everyone, but what about when there are more variables with some relationship between them which is hard to notice without computing?