# Regression: average as dependent variable

Although I saw a few similar threads, I don't believe I saw the specific answer to the following question: If your dependent variable is an average are any assumptions violated?

Let me give you some more details on what I plan to do: I am interested in detecting the effect of some policy (a treatment) on cheating in exams. A simple identification strategy would work as follows:

1. Calculate the number of similar answers $Y$ for each pair of neighbors
2. Consider each individual $i$. For example, individual $i=1$. This guy was sitting next to individuals $i=2$ and $i=3$. For each student $i$, calculate the average number of similar answers over both neighbors $\overline{Y}_i$.
3. Run the following regression: $$\overline{Y}_i = \beta_0 + \beta_1 Treatment\_Dummy_i + u_i,$$ where $\beta_1$ identifies the treatment effect on the average number of similarly answered questions. Put differently, the treatment was randomized.

My question: I wonder whether this can be done? Would I get biased standard errors in this example? Are other assumptions violated?

Thank you very much!

• Can you be more concrete about what your dependent and independent variables are and how you computed the average ? – user83346 Sep 21 '17 at 13:46
• Thank you for this quesion. I will clarify my initial post. – bachelor Sep 21 '17 at 14:09
• How do you define the dummy ? – user83346 Sep 22 '17 at 6:12
• The dummy is 1 if an individual is part of the treatment group and zero otherwise. Individuals are randomly allocated to the treatment and control gruop. – bachelor Sep 25 '17 at 6:34