What type of analysis do I need to understand and/or gain information from a set of data?
For example, I have students' data for SATScore, HighSchoolGPA, HighSchoolRank, etc., and FreshmenGPA.
Now I want to develop a model which tells me which of the criteria are important for FreshmenGPA and by how much. I want to quantify the importance of these categories (SATScore, HighSchoolGPA, HighSchoolRank, etc.).
What options do I have? Which is the most accurate methodology to do such analysis?
What I Want to find out from the data:
I want is to identify which of these variables(SATScore, HighSchoolGPA, HighSchoolRank, etc.) can help me predict Students FreshmenGPA.
I did some reading on what I need to do for this but there is no definite source or a definite answer. From what I roughly understand, it looks like I need to find out which of these variables are helpful in predicting FreshmenGPA, and whether there is an interaction variable(combination of two or more variables) which is a better predictor than any individual variable. How can I do this?
Once I know which variables and/or interaction variables are important for my model, I will need to quantify the variable importance, for this I'll need to find out the weights(coefficients) for variables which I found are important for FreshmenGPA. Could anyone show me the steps I need to follow to understand and do this? Also, It looks like there are multiple ways of doing this, Not sure if this is correct, but If so which of these methods give the most accurate model for the data?