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1. Consider the following linear regression model: (a) Which assumptions are needed to make the B, unbiased estimators for the B, (b) Explain how one can test the hypothesis that A +As = 0 by means of a t-test. (c) Explain how one can test the hypothesis that A-A-0. Indicate the relevant test statistic. (d) Suppose that ri is an irrelevant explanatory variable in the population model and that you estimate the model including both and r2. What are the consequences of estimating this model? e) Suppose instead that is a binary explanatory variable. Which is the interpretation of the paraneters A), β1 and β2 in this case? f) Suppose again, as in point (e), that 1 is a binary explanatory variable and that one also adds the interaction term x1 × x2 among the regressors. Let 1 to be the coefficients of the interaction term. Discuss the interpretation of the coefficients under these assumptions.

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