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2007 Midterm Exam 2

# 2007 Midterm Exam 2 - Midterm Exam 2 Econ 360 Fall 2007...

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Midterm Exam 2 Econ 360 - Fall 2007 Professor Mumford Thursday, November 1, 2007 [email protected] RAWL 2077 3:00 – 4:10pm YOUR NAME: Answer all questions clearly and legibly. Show all of your work in the space provided. Do not use additional sheets or write on the back of the page. Do not refer to your notes, the text book, or any other materials during the exam. There are 100 points possible. Maximum points for each question are noted in parentheses. You have one hour and ten minutes to complete the exam. Good luck! 1. (15 points) Define or explain the following terms: a. (3 points) beta coefficients b. (3 points) adjusted R-squared c. (3 points) F statistic d. (3 points) heteroskedasticity e. (3 points) p value

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2. (12 Points) a. (4 points) State assumption E.5 (Normality) b. (4 points) Under E.1 - E.5, what is the distribution of ˆ β ? c. (4 points) Without assumption E.5, when are t-statistics valid? Explain.
3. (12 Points) a. (8 points) In the multiple regression model, derive the variance-covariance matrix of the OLS estimator under E.1 - E.4. Recall that ˆ β = ( X 0 X ) - 1 X 0 y . Indicate the role of assumption E.4 (Homoskedasticity and No Serial Correlation). b. (4 points) Assume that Var ( u | X ) = σ 2 H , where H = h 1 0 · · · 0 0 h 2 · · · 0 . . . . . . . . . 0 0 · · · h n . What is the variance-covariance matrix of the OLS estimator under assumptions E.1- E.3 and the assumption stated above?

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4. (23 Points) Purdue announces a plan to give a laptop computer to every student starting next year. You are asked to predict the likely effect of this policy on student GPA. You conduct a survey of 1,000 Purdue students and you also obtain their administrative records. From the administrative records you know the current GPA, the number of credits completed, major, gender, SAT score, and high school GPA. In the survey you ask these students whether or not they own a laptop computer and whether or not they own a desktop computer. You also ask about the amount of time they spend studying, sleeping, relaxing, and doing other activities. a. (5 points) Write a model (in equation form) that would allow you to estimate the effect of owning a laptop computer on college GPA, while controlling for gender, SAT score, and the number of credits completed. You should be able to make a statement of the form: “laptop ownership is estimated to increase college GPA by a certain percentage.” Describe each variable in your equation and how you generated it from the data provided. b. (5 points) Write a model (in equation form) similar to the equation in part (a) that would allow you to test whether those who only have a laptop have a higher GPA than those who only have a desktop computer. State the null hypothesis and explain how you would preform the test.
c. (4 points) What is the effect of an additional hour of study on GPA in the following model? Also, explain what a positive value for β 4 means.

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2007 Midterm Exam 2 - Midterm Exam 2 Econ 360 Fall 2007...

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