# ProblemSet3 Answers - Professor Mumford Econ 360 Spring...

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Unformatted text preview: Professor Mumford Econ 360 - Spring 2010 [email protected] Problem Set 3 Answers Multiple Choice Questions (12 points) Suppose that a random sample of 200 male students is selected from Purdue’s student population. These mens’ weight (measured in pounds) is regressed on their height (measured in inches) with the following result: d weight =- 100 + 4 height n = 200 R 2 = . 8100 1. What is the predicted weight from this regression for someone who is 5’10” (70 inches) tall? (a) 380 (b) 280 (c) 200 (d) 180 2. Suppose that instead of measuring in pounds and inches, we measured in pounds and feet (5.833 feet instead of 70 inches). What would be the estimated intercept? (note that 12 inches = 1 foot) (a) -8.333 (b) -12 (c)-100 (d) -1200 3. Again, suppose that instead of measuring in pounds and inches, we measured in pounds and feet. What would be the estimated coeficient on height ? (a) 0.333 (b) 4 (c) 12 (d) 48 1 4. Suppose that instead of measuring in pounds and inches, we measured in kilograms and inches. What would be the estimated intercept? (note that 1 pound = .454 kilograms) (a) -0.454 (b)-45.4 (c) -100 (d) -220.26 5. Again, suppose that instead of measuring in pounds and inches, we measured in kilo- grams and inches. What would be the estimated estimated coeficient on height ? (a) 0.454 (b) 1.816 (c) 4 (d) 8.811 6. Suppose that instead of measuring in pounds and inches, we measured in kilograms and feet. What would be the new R-squared? (a) 0.0675 (b) 0.2700 (c) 0.3677 (d) 0.8100 True/False (6 points) 7. TRUE In the simple linear regression model, the homoskedasticity assumption means that the error, u , has the same variance given any value of the explanatory variable, x . 8. FALSE The standard error of the regression (SER) is denoted as ˆ σ . It is also known as the root mean squared error. The standard error of ˆ β 1 = ˆ σ/ (∑ n i =1 ( x i- ¯ x ) 2 ) 1 2 9. TRUE The OLS residual for observation i is defined as ˆ u i = y i- ˆ y i . 2 10. Variance of the OLS Estimator in the Simple Linear Regression Model ˆ β 1 = n X i =1 ( x i- ¯ x ) y i n X i =1 ( x i- ¯ x ) 2 ˆ β 1 = n X i =1 ( x i- ¯ x )( β + β 1 x i + u i ) n X i =1 ( x i- ¯ x ) 2 ˆ β 1 = β n X i =1 ( x i- ¯ x ) n X i =1 ( x i- ¯ x ) 2 + β 1 n X i =1 ( x i- ¯ x ) x i n X i =1 ( x i- ¯ x ) 2 + n X i =1 ( x i- ¯ x ) u i n X i =1 ( x i- ¯ x ) 2 ˆ β 1 = β 1 + n X i =1 ( x i- ¯ x ) u i n X i =1 ( x i- ¯ x ) 2 Var ˆ β 1 = Var β 1 + n X i =1 ( x i- ¯ x ) u i n X i =1 ( x i- ¯ x ) 2 β 1 is a constant Var ˆ β 1 = Var n X i =1 ( x i- ¯ x ) u i n X i =1 ( x i- ¯ x ) 2...
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ProblemSet3 Answers - Professor Mumford Econ 360 Spring...

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