Please keep answers brief and to the point.

1) When we run a regular regression to test the null hypothesis that X has no impact on Y, you may get the following results presented to you. In each case, explain how you would deduce whether or not to reject the null hypothesis with at least 95% confidence - if you have to do the calculations, explain what they would be. Assume the sample you use to run the regression is large (over 1000 observations). a) The coefficient estimate of X and the corresponding standard error. b) The coefficient estimate of X and the corresponding t-statistic. c) The coefficient estimate of X and the corresponding p-value. d) The coefficient estimate of X and the corresponding 95% confidence interval. 2) a) What is the key difference in interpreting the coefficient estimate of a "treatment" on an outcome in a randomized controlled trial, versus trying to interpret the coefficient estimate of the same treatment on the same outcome in observational, cross-sectional, retrospective data where the scientist had no control over who selected to get the treatment and who did not ? b) Briefly (bullet points are fine) describe the key features of setting up a simple difference-in-difference model and explain how it tries to improve on findings you would get from just a cross-sectional analysis in the post-treatment period. Also, briefly describe (use a diagram if necessary) the importance of the "parallel trends assumption" in simple difference in difference.

3) A study is being planned to test whether Medicaid expansion led to more low-income adults having access to primary-care physicians. The study will use data from all states, collected annually over 2010-2022, and estimate regression models where the outcome variable, Y, will be the percentage of low-income adults under 65 years in the state who have a primary care doctor. The main X variable of interest will be a binary indicator of whether that state has adopted the policy of extending Medicaid coverage to all low- income adults (1 if yes, 0 if no). The plan is to use two-way fixed effects (state and year), and to explicitly include variables that are TIME-VARIANT for states during this time period. For each of the variables listed below, choose from (I) fully controlled for by state fixed effects; (II) fully controlled for by year fixed effects; (III) not fully controlled for by either,

so should include variable in model if it is available. (Basically a multiple choice question, you are not required to explain your answer). a. Whether or not President Obama won the state in the 2008 elections. b. The distance of the state from Mexico. c. The annual state poverty rate. d. The number of physicians in that state who were accepting Medicaid patients that year. e. The annual national GDP growth that year. f. Whether the National Public Health Emergency due to COVID19 was in effect. g. The party affiliation of the governor of the state. h. Whether it is a presidential election year.