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Midterm_2_study_questions(2008)

# Midterm_2_study_questions(2008) - ECG 561 Intermediate...

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ECG 561, Intermediate Econometrics, Spring 2008 Study Questions for Midterm II 1. Consider the following multiple regression: y i = + 1 x 1i + 2 x 2i + u i , where the basic assumption about the error term hold. Describe in detail how you could test the following hypotheses using the F-statistic that compares a restricted with an unrestricted regression model. (a) 2 = 2 (b) 1 = 2 (c) 1 = 2 2 (d) 1 + 2 = -1 (e) + 1 + 2 = 0 (f) 1 = 2 = 5 2. A researcher estimates a multiple regression, in which y is the dependent variable and x 1 and x 2 are the independent variables. The researcher suspects that a basic assumption concerning the disturbance terms is violated for the data he is examining. Namely, he suspects that: Cov(x 1 ,u) 0. He proposes to test the hypothesis by calculating the sample covariance between x 1 and . If the sample covariance is far enough from zero then he proposes to reject the null hypothesis of uncorrelated x 1 and u. What is wrong with his test procedure? 3. True, False, or Uncertain (and explain): In a simple linear regression, if the t-statistic for the slope coefficient equals zero, then the R 2 for the regression equals zero, and the F-statistic for the regression equals zero. 4. True, False, or Uncertain (and explain): In a simple linear regression, the t-statistic for the slope equals the overall F-statistic for the regression. 5. True, False, or Uncertain (and explain): If the R-squared for a simple linear regression is zero, then the F- statistic testing H o : o = 1 = 0 will also be zero. 6. You run a linear regression of corn yield (y) on fertilizer level (x), assuming the standard linear regression model discussed in class. When you present your research results to your thesis committee, you are asked to perform two calculations: (i) Estimate the expected corn yield that would result from an application rate of 400 pounds per acre and construct a 90% confidence interval around your estimate–an interval that in repeated sampling would contain the true conditional expectation 90% of the time. (ii) Predict the corn yield that would result from an application rate of 400 pounds per acre and construct a 90% confidence interval for the realized corn yield–an interval that in repeated sampling would contain the realized corn yield 90% of the time. Explain why the confidence interval that you would construct in (ii) would be larger, perhaps much larger, than the confidence interval you would construct in (i). Your answer should be primarily in words, but you may use relevant formulas as well.

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2 7. Consider the regression of prate on rate in Problem Set #3. The variable prate is a percentage with values in the range 3 to 100. The variable rate
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Midterm_2_study_questions(2008) - ECG 561 Intermediate...

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