# Regression with or without controlled variables?

I wanted to see the impact of small business support programs on small business growth. I regressed their growth (represented by the number of employees) on only those 5 kinds of support programs (as regressors). and I found R squared= 0.35, adjusted R squared= -0.03, some coefficients are positive while some others are negative, and all the p-values is > the significance level (10%) (coefficients are insignificant). 1) May I conclude that the support programs have a positive but insignificant effect? 2) Should I include control variables to complete the model (so that r squared become > 0.5).

• The negative adjusted R squared is concerning. This usually happens when one tries to fit too many predictors into a model that uses very few number of cases. What is your sample size? And totally how many predictors do you have in your model? – Penguin_Knight May 29 '13 at 19:08

## 1 Answer

First, you will likely never "complete the model."

1) Yes--insignificant with your analysis's current level of statistical power. No--not all positive, according to your statement that "some coefficients are positive."

2) Unclear where you are getting the ".5"; perhaps you have already tried an additional set of variables and with them increased RSQ beyond that level. But it's not a matter of "should"; it's a question of what you want to investigate and what you want to show. Control "shouldn't" be applied merely because you can but should be used when you want to know how, and how strongly, certain variables relate to the outcome while certain other variables are accounted for / held constant / partialled out. It makes sense to control for other variables if you want to assess the relationship of set B* to the outcome with set A already "in place," and/or if you want to see to what degree of accuracy set B can predict the outcome beyond the accuracy obtained with set A. This is seldom as easy a decision as certain texts make it out to be, and I encourage you to read widely on control and to visit threads on this site tagged 'statistical control', 'partial correlation', and 'suppressor'.

*I say "the relationship of set B to the outcome" rather than the relationship of each member of set B. This is because, with enough collinearity, you won't reliably be able to estimate each variable's true relationship; each coefficient will be affected by the presence of all the other covariates. So statistical control can occur, and its related problems can apply, within a block of variables just as between different blocks.