Question:

Consider the model \(Y=B_{0}+B_{1} X_{1}+B_{2} X_{2}+e\), e \(\sim \mathrm{N}\left(0, \sigma^{2}\right)\) where the 'xs are all continuous variables. You also have data on a qualitative variable denoted \(d_{1}\) for each observation, where \(d_{1}=1\) if the observation belongs to group 1 , and zero otherwise. a. [3 pts] Assume you want set an empirical model to see the expected value of \(Y\) was different for members of group 1 . What model, null, and alternative hypothesis would you need to estimate and test, assuming identical continuous variable values? Show your work and explain. (Hint: add dummy variable)

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