I have an interesting operational situation at hand. I have a dependent variable, let's call it variable Y and a set of independent variables: V, H, N. (relationship is based on my operational knowledge) There may be a couple of variables at most that I may not know of. I have data for all these variables.
My first challenge is to prove that my dependent variables are correlated with V, H and N (in linear or non-linear way). How can I do this? I know I can use correlation analysis in Excel, but are there any other ways wherein I can determine the power of the independent variable as well?
My Second challenge is to prove that the independent variables are mutually not or minimally correlated. Operationally I know they aren't. So it shouldn't be difficult to prove once I have their right power in relation to Y.
My third and most difficult challenge is to determine, the exact multi-dimensional equation that defines the relationship between Y and V,H,N (separate problems).
I can use regression, but only when I have the right exponents for the independent variables. Any other method is welcome.
I do have the input and output data. A Lot of it.
I would really appreciate an insight on this issue.