Consider a simple linear model Yi = 1 + 2Xi + ui . Suppose that we have a sample with 50 observations and run OLS regression to get the estimates for 1 and 2. We get 2 = 3.5, P N i=1 (Xi X) 2 = 175, T SS = 560 (total sum of squares), and RSS = 340 (residual sum of squares).

1. [2 points] What is the standard error of 2?

2. [4 points] Test the null hypothesis H0 : 2 = 3 against the alternative hypothesis H1 : 2 6= 3 (use 10% significance level).

3. [4 points] What is the 90% confidence interval for 2? 1

4. [2 points] How do we measure the goodness of fit of a regression? What can you say about the goodness of fit of this regression given the information above?