In: Statistics and Probability
Consider the case of three treatment status, where we have no treatment, treatment 1 and treatment 2. Let d1 be a dummy variable taking 1 for treatment 1 and 0 otherwise, and d2 be a dummy variable taking 1 for treatment 2 and 0 otherwise.
We consider the following regression
y = α + βd1 + γd2 + ε,
where α, β and γ are parameters and ε is the error with E[ε] = 0. Using β and γ in this regression, explain what you can estimate First, express only the final outcomes mathematically (no derivations) and second, explain each (no more than 10 words for each).