I am working on a prediction problem. I have a programming background and a small statistics one. If I have two dependent variables and one independent one, how do I work out if the two are co-related?
For example, x1 has a correlation coefficient of .6 and x2 has one of .4. I hypothesize that x1 and x2 are not totally dependent (identity) and not totally independent to each other. Is there a way to analyze this situation mathematically to eventually decide weights of a final regression equation?
I suppose I could put one x into bins and make a piecewise equation based on certain cutoffs. But, this seems not to be optimal and in reality there are many x's. I have not found any good literature on how to differentiate weights of dependent variables. I know machine learning is designed for this but I would like a 'old school slide ruler' approach where I can understand the differences of variance.
I am in a exploratory phase where given two (and really many more) variables figure out the outcome. If the two variables are co-related then some of the variance is overlapping. I would like to know how much overlaps and how to weight the variables in an ending regression equation. (this my not be the right terminology so please bear with me.)