# Dummy Variables in a Regression setting

I have data with several dummy variables $\{x_1,...,x_k\}$ and a dependent variable $y$. Imagine I want to do an analysis with just a subset of the dummy variables $\{x_{\pi_1(1)},...,x_{\pi_m(k)}\}$. Should I use all the observations of the dependent variable $y$, or just those that belong to the subset of dummy variables $\Pi(y)$? Why?

I know that the OLS estimates in both possibilities will be equal, but not the standard errors, which will give me different confidence intervals, t-statistics, etc.

For example: My $y$ is income of a given sample of individuals, which are divided among 3 non-intersecting groups(G1,G2,G3). Let's suppose I want to run a regression of income on $\text{Dummy}_{G3}$ only. Should I use $y$, or $y_{G3}$ i.e. only the income corresponding to individuals in G3?

G1  G2  G3  Income
0   0   1   569.5
0   0   1   895.5
0   0   1   1111
0   0   1   1182
0   0   1   1277.5
0   0   1   1384
0   0   1   1464.5
0   0   1   2453
0   0   1   2538
0   0   1   2539.5
0   0   1   2830.5
0   0   1   2852
0   0   1   2865
0   0   1   2945
0   0   1   3023
0   0   1   3024.5


The data continues. I have approximately 4500 observations. $\text{Dummy}_{G1}+\text{Dummy}_{G2}+\text{Dummy}_{G3}=\mathbf{1}$

Any help would be appreciated.

• if you used a complete data set, what would be the values of a subset in it? Are they missing? What do you mean by "belong to" in this context? Commented Apr 2, 2016 at 13:23
• When you say "all the observations of the dependent variable $y$", do you mean all of the dummy variables? Commented Apr 2, 2016 at 13:38
• @Aksakal I'm not sure I understand what you're asking. I've edited the question. Commented Apr 2, 2016 at 13:39
• @caveman I've edited the question. Commented Apr 2, 2016 at 13:39
• show an example of data set, a few rows maybe. it's still not clear what's up with dummies in three subsets. Commented Apr 2, 2016 at 14:01