# ps2_ak - Problem Set 2. ANSWER KEY Introduction to...

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Problem Set 2. ANSWER KEY Introduction to Econometrics - Fall 2006 Due Date: Thursday, October 5th, BEFORE CLASS. Each student is responsible for handing one handwritten solution. If working in groups, indicate the members of the group (to facilitate grading). PLEASE SHOW YOUR WORK . 1. A random sample of 400 ants is taken from an anthill and their length and speed are recorded. Length is measured in inches and speed in miles per hour. A regression of speed on length yields: \ speed = 1 : 1 + 4 : 28 ± length R 2 = 0 : 92 SER = 15 : 1 1 : 2 inches long. What is the regression speed prediction for it? What if it was 0 : 5 inches long? Solution: \ speed = 1 : 1 + 4 : 28 ± 1 : 2 = 4 : 036 m=h and in the second one \ speed = 1 : 1 + 4 : 28 ± 0 : 5 = 1 : 04 m=h . (b) If an ant grew by 3 inches, how much would its regression predicted speed increase? Solution: In order to answer this, we only need to take into account the estimate for the slope. Then, we know that the increase in speed will be of 4 : 28 m=h ± change in lenght = 4 : 28 m=h ± 3 = 12 : 84 m=h . (c) Now, say that length was recorded in centimeters and speed in kilometers per hour. What are the regression estimates from this new regression? (Specify all estimated coe¢ cients, R 2 and SER ) 1 Solution: Say that the lenght = 0 : Then, \ speed = 1 : 1 m=h = 1 : 1 ± 1 : 6 km=h = 1 : 76 km=h: Next, say that lenght increases by 1 inch . Then, \ speed increases by 4 : 28 m=h: That±s equivalent to an increase of 4 : 28 ± 1 : 6 km=h = 6 : 848 km=h: To sum up, when lenght increases by 2 : 5 cm; then speed increases by 6 : 848 km=h: Then, when lenght increases by 1 cm; speed increases by 6 : 848 km=h 2 : 5 = 2 : 7392 km=h . To sum up: \ speed = 1 : 76 + 2 : 7392 ± lenght Note that the R 2 does not change, since it has no dimension. On the other the side standard error of the regression is an estimator that has the same unit as the speed: Consequently, the new SER will be 15 : 1 ± 1 : 6 = 24 : 16 . to complete the exam while others have 120 minutes. Each student is randomly assigned one of the examination times based on the ²ip of a coin. Let Y i denote the number of points scored on the exam by the i th student (0 ² Y i ² 100) , let X i denote the amount of time that the student has to complete the exam ( X i = 90 or 120) , and consider the regression Y i = & 0 + 1 X i + u i : (a) Explain what the term u i represents. Why will di/erent students have di/erent values of u i ? Solution:

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## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.

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ps2_ak - Problem Set 2. ANSWER KEY Introduction to...

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