# What does “arrived at linear multiple regression models” mean?

I'm reading a paper on a study where a number of respondents received questions which they graded using a scale of 1-5. In the conclusion, the authors wrote that they "arrived at linear multiple regression models for the consolidated dependent variable N". What does that mean?

(Disclosure: I am not a student of mathematical stats, so please use layman's terms)

• "arrived at" just means "decided to use". "consolidated dependent variable N" means they constructed the dependent variable (e.g. perhaps from several raters, each rating 1-5 -- impossible to say from what you wrote so far). "linear multiple regression" is a standard statistical technique; I'm not good enough to explain this in the characters I have left. – zbicyclist Dec 5 '11 at 17:12
• +1 zbicyclist: Should make it an answer -- unless you're too new to be able to do that. Get full credit for a good answer. – Wayne Dec 5 '11 at 18:20

I guess the answer to this question can be very complex but I'll try to give a general idea of how "arriving at a model" works:

You have your outcome (the dependent variable) that you want to correlate different variables to. The problem is that if you have 5 observations, let's say patient height, then if you have a couple of variables you might risk that by combining two-three different variables each patient will get a unique combination generating the "perfect model". This is basically the same as knowing each patients name and checking their height in their chart. This is what is known as overfitting and the general problem with multiple regression.

Usually you need some kind of restriction so that this doesn't occur. There are different approaches to address overfitting the basic idea is that when you look how much each variable contributes you also punish that value by adding that variable, AIC and BIC are common measures for this. I'm currently working my way through Frank Harrel's book on Regression Modeling Strategies that is a very nice in-depth description of different methods.

Another important part is to use already known confounders. If previous similar studies have shown that gender has a big impact in the new study should probably have at least tested that variable.