Consider a simple linear model Yi = β1 + β2Xi + ui . Suppose that we...

Consider a simple linear model Yi = β1 + β2Xi + ui . Suppose that we have a sample with 50 observations and run OLS regression to get the estimates for β1 and β2. We get βˆ 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 βˆ 2?

2. [4 points] Test the null hypothesis H0 : β2 = 3 against the alternative hypothesis H1 : β2 6= 3 (use 10% significance level).

3. [4 points] What is the 90% confidence interval for β2? 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?

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orchestra answered 1 year ago

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