CalssTestS2v25-v2.pdf - Name ID Version 2 ETC2410 ETC3440...

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Name: ID: Version 2 ETC2410 - ETC3440 - ETW2410 Introductory Econometrics Mid-Semester Test - 31 August 2016 Circle the option that is the best answer to the question out of the 5 choices provided. If you circle more than one option for a question, you get zero for that question. Random variables Y and X have the following joint probability density function. Y , X 1 0 1 0 . 6 0 . 2 0 0 . 0 0 . 2 . Answer questions (1), (2) and (3) with reference to this joint density. 1. E ( Y ) is (a) 0 . 5 (b) 0 . 6 (c) 0 . 25 (d) 0 . 8 (e) none of the above [1 mark] 2. E ( Y | X = 0) is [1 mark] 3. E ( X | Y = 1) is: [1 mark] Page 1 of 8
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4. Last semester, there were 300 students taking this unit. The average mark on the mid- semester test was 12 (out of 20). Suppose instead of reporting the raw score, I had reported the “deviation from the average” mark to each student, that is, reported +2 to a student who got 14, and -3 to a student who got 9. The average of these “deviation from the average” marks would be: (a) 12 300 = 0 . 04 (b) 12 (c) positive if more than half of the class got above the average mark, negative if more than half of the class got below the average mark, and 0 if exactly half of the class scored above the average and the other half scored below the average. (d) positive if the distribution of raw marks was skewed to the right, 0 if the distribution was symmetric, and negative if the distribution was skewed to the left (e) 0 [1 mark] 5. Consider random variables x and y with population means μ x and μ y . Which one of the following is not equal to Cov ( x, y ): [1 mark] 6. A radio host who travels to work by train every morning at 6 am, has counted the number of people in the same train carriage as him who carry an umbrella every day for two years. He has also collected data on the total amount of rainfall on each of those days. He has estimated a simple regression with rainfall as the dependent variable and number of umbrellas as the independent variable and has found a very good fit. Using the estimated model, he starts his morning radio program by predicting rainfall on that day based on his count of people carrying umbrellas on the train earlier on that day. Which of the following statements is true: (a) his regression does not provide a good estimate of E (rainfall | number of umbrellas) because of omitted variable bias (b) his regression provides a good estimate of E (rainfall | number of umbrellas) (c) his predictions are not good because of heteroskedasticity (d) his predictions are useless because carrying an umbrella does not cause rainfall (e) his predictions are biased because of prefect multicollinearity [1 mark] Page 2 of 8
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