Maybe you can help me with some logic on this. run this regression analysis twice. The first time I ran it with two variables, but I realized that the first variable was actually the product of two other variables, so I separated it out into it's respective pieces and re-ran the numbers, which are what I posted in the first post.
Here are the R-squared measurements of some variables from each formula:
X2 became more descriptive than X1, which makes sense because I pulled out the irrelevant part by segregating variable Z. However, the original combination of X1 and Y was actually more descriptive than X2 and Y in the new equation, and that makes absolutely no sense to me.
Can anyone explain how making one variable more descriptive actually made the combination of that variable and a constant less descriptive in the new formula?
It has to do with how the two variables are related. In this situation it may be that while X2 is the best predictor by itself, X2 and Z don't work as well together as X1 and Z.
It may be that Z is actually more related to X2 than it is to X1. So adding Z as a predictor with X2 doesn't actually add that much to the prediction. However, adding Z as a predictor along with X1 actually adds quite a bit to the analysis.
The whole thing is really confusing and hard to understand. It doesn't always make sense. Stats is a fickle, fickle being...