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?

  • $\begingroup$ Your tags suggest that you already know a short answer here, multiple regression. It's not quite clear what kind of answer you expect otherwise. $\endgroup$ – Nick Cox Aug 13 '13 at 18:07
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    $\begingroup$ Sometimes the answer is wait, but my main comment remains that it's not clear what you expect here. No one is likely to write a long essay on what you might do. Probably more than half statistics falls under your very general title. So, try to make it much more specific. What do you next want to know? $\endgroup$ – Nick Cox Aug 13 '13 at 19:21
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    $\begingroup$ While you are waiting, you should consider looking over the other threads with the model-selection (and maybe multiple-regression) tags. I'm pretty sure your question has already been fully and elaborately answered. $\endgroup$ – whuber Aug 13 '13 at 20:27
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    $\begingroup$ "enough" means that someone will answer in a way that satisfies you; that's doubly difficult to predict. As @whuber advises, do look at what's already on-site. $\endgroup$ – Nick Cox Aug 13 '13 at 21:06
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    $\begingroup$ As a somewhat recent graduate I know the following: you do not have enough measures to determine success. With incomplete data you are going to have imperfect results. How do you account for the friends they make? (rf?) How do you measure the party culture on campus? What happens if they get their heart broken? GPA doesn't have enough information to tell you those "why" answers to the question of freshman GPA. It doesn't speak to proper match of aptitude and interest with course selection. Emotional baggage. Teen angst. $\endgroup$ – EngrStudent - Reinstate Monica Sep 10 '13 at 13:07

As was noted, your question is very general, and as such there are MANY different approaches.

  1. Perform linear regressions on y ~ x (y=one variable only) with FreshmanGPA as your dependent variable. The weights of each variable explain the interactions. Looking at the p-values will determine if the variable is likely to be useful (low p-values are better).
  2. Calculate the correlation between FreshmanGPA and all other variables. The variable with the highest correlation is the most associated with FreshmanGPA. Then go back and run the linear regression on this variable.
  3. Run a discriminant analysis on all the data, calculating for FreshmanGPA. The coefficient size are proportional to the predictive power of the variable.
  4. Run linear regression on the interaction terms and compare how the model performs compared to a single variable.

These are only a few ideas. The calculations can be done in many different programs, such as R, SAS, Stata, and many others that I am not familiar with.

In order to compare which factor is the most important, you are basically looking for a relationship that either (1) explains the current data the best. That is to say, if you have a linear regression, your residual errors is the smallest, or (2) predicts a new dataset the best. For (2) you will need to split your data into a testing and training sample. Each time you run a training model, you then predict the FreshmanGPA on the testing sample and see how close you are (the residual error).

Which you choose depends on the purpose of the test. From the question, I expect the first option is better suited.

For detailed examples on how to run this, you will need to specify what program you are using, and give an example of the dataset. Try searching within the forum for a few specific terms. For example:

  • linear regression R (SAS, Stata, etc)
  • Discriminant Analysis
  • Comparing linear regressions
  • How to calculate interaction terms in R (SAS, Stata, etc)
  • $\begingroup$ Is there some analysis we can perform to show what % of dependent variable is explained with data we have? and also show a confidence interval for our estimate. for e.g This data describes 60% of dependent variable(GPA) and we are 90% confident about it? $\endgroup$ – user793468 Sep 17 '13 at 1:56
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    $\begingroup$ For the percent explained, it depends on the type of study you use, but all options will present this information. For example, linear regression will tell you the amount of deviance explained by each variable. A discriminant analysis will tell you the amount of variance explained by each axe (which is a combination of different variables). Confidence intervals can be made on the estimates of the variables (how correct are we?), and it usually requires more assumptions on the data. I would suggest creating a new question once you've decided what method to use to get a specific answer. $\endgroup$ – Drew75 Sep 18 '13 at 9:56

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