Download Midterm Exam in Introduction to Econometrics: Spring 2008 and more Exams Introduction to Econometrics in PDF only on Docsity! ECON 4241524 Introduction to Econometrics Form A Midterm Exam Spring 2008 C. Tremblay Instructions: This exam is worth 120 points. Point values for each question are indicated to the right of the question number. All students will answer questions 1-6. (This time, there are no separate questions for ECON 424 and ECON 524 students.) Calculators, books, and other notes are not allowed. A t-table is attached at the back. Please show your work. Good luck. 1. (14 points) Suppose that you want to find out the effect of gas prices (PG) on the price of s u v s (PS). a. Write down a sample regression model that would allow you to estimate the effect of gas prices on SUV prices. b. Based on your estimated model, how could you calculate the elasticity of SUV prices with respect to gas prices? c. How would you predict the price of SUVs if gas prices were $4 per gallon? 2. (32 points) The regression results below are from data on swim meet results on 140 races (Emerald Aquatics January 10, 2004 meet, Eugene, OR). The variables are: seed = seed time (the swimmer's estimate of race time prior to the race) in seconds final = final time in seconds Dependent Variable: final Analysis of Variance Source Sum of Mean D F Squares Square F Value Pr > F Model 1 6 5 9 7 8 1 1 6 5 9 7 8 1 1 8 8 5 5 . 6 7 c . 0001 Error 1 3 8 102815 7 4 5 . 0 3 8 0 1 Corrected Total 1 3 9 6700626 Root MSE 2 7 . 2 953 8 R- Square 0 .9847 Dependent Mean 1 5 2 . 1 3 5 2 9 Adj R-Sq 0 .9845 Coeff Var 17 .94152 Parameter Estimates Parameter Variable DF Estimate Standard Error t Value Pr > It 1 Intercept 1 3.39240755274047 2 .79643284018174 1 . 2 1 0 .2272 seed 1 1.00016488225905 0 . 0 1 0 6 2 8 2 2 8 6 7 6 2 1 9 4 . 1 0 c . 0 0 0 1 a. Write down the estimated regression equation (you may round to 2 decimal places). n, f , rrnl = 3.39 + t.00 ,seed b. Graph the estimated regression. Be sure to label axes, intercept and slope. Use actual numbers and variable names (e.g., not just x and y). 6. (20 points) a. Simplify the following expressions, where x is a random variable and a and c are constants: 1. E(c) = C Y var(a+cx)= \ / a - C l q ) + V C ~ ~ ( C X ) = cZ \/w+ I x ) 11. b. Let XI, 33, - . ., xT be a random sample of independent observations from a population with mean p and variance c2. Consider the following estimators of p: - O Is x an unbiased estimator of p? Prove your answer. O Is % an unbiased estimator of p? Prove your answer. 0 Which estimator has a lower variance? How do you know? @ Which estimator would you choose to estimate p? Why? O Y e s . h @ 'Yes. E I T ; z ELL h A ~ J j=) ~ ( 2 ) = E l i *, + $71 - - - I E[&$) iz 1 L\ - -L E IY,) 4- 1 ~ ( f l = I 25 ~ ( $ 3 z z fi , h - - - ,k +LA - l - 2 ~ a- 2- V\ ;=, E [ 2 ) = A * = ~ ( n k ) 14 5- n e x t p ~ j e for dwi ~ ~ r h ' a b s . @ b@ Continved
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