# ps4 - Problem Set 4 Introduction to Econometrics - Fall...

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Problem Set 4 Introduction to Econometrics - Fall 2006 Due Date: Tuesday, November 7th, 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. Consider the following multiple regression model: Y i = β 0 + β 1 X 1 i + β 2 X 2 i + u i You collect a random sample of 1000 observations and you estimate following regression: b Y i =2 . 52 (1 . 12) +1 . 25 (0 . 95) X 1 i 0 . 89 ( . 64) X 2 i R 2 =0 . 22 Assume that all the lest squares assumptions hold. (a) Estimate the expected change in Y i when X 1 i is increased by 1 unit and X 2 i is constant. Estimate the expected change in Y i when X 1 i is constant and X 2 i is decreased by 2 units. Estimate the expected change in Y i when X 1 i is decreased by 2 unit and X 2 i is increased by 1 units. (b) Compute the R 2 of this regression. 2. Consider the following multiple regression model: Y i = β 0 + β 1 X 1 i + β 2 X 2 i + u i where E ( u i | X 1 i ,X 2 i )=0 . (a) Assume X 2 i =2+ X 1 i . Can you compute the OLS coe cients? Explain. (b) Assume again that X 2 i =2+ X 1 i . Can you write a single variable model: Y i = δ 0 + δ 1 X 1 i + u i , equivalent to the multiple regression model above? Can you compute the OLS coe

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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 University of Wisconsin.

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ps4 - Problem Set 4 Introduction to Econometrics - Fall...

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