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slides_lecture6 - ECON 103, Lecture 6: The linear...

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Unformatted text preview: ECON 103, Lecture 6: The linear regression model (contd) Maria Casanova April 16th (version 1) Maria Casanova Lecture 6 Requirements for this lecture: Chapter 4 of Stock and Watson Maria Casanova Lecture 6 1. Introduction Suppose we are interested in estimating and 1 in the following model: Y i = + 1 X i + i We may estimated the unknown and 1 by OLS: = Y- 1 X 1 = X i ( X i- X )( Y i- Y ) X i ( X i- X ) 2 Next we review the assumptions on the linear regression model and the sampling scheme under which OLS provides an appropriate estimator of and 1 . Maria Casanova Lecture 6 2. The least squares assumptions Ass1: The conditional distribution of i given X i has a mean of zero. E ( i | X i ) = 0 This is a statement about the underlying model. This assumption refers to the other factors affecting Y i which are captured by i . It says that these other factors are unrelated to X i in the sense that, given a value of X i , the mean of their distribution is zero. Maria Casanova Lecture 6 2. The least squares assumptions Figure: Conditional mean wage given fitness 1 2 3 4 5 6 7 8 9 10 500 1000 1500 Fitness Wage Population regression function1 + 1 X 1 X 1 = (lowest) (highest) Maria Casanova Lecture 6 2. The least squares assumptions Figure: Conditional mean wage given age 20 25 30 35 40 45 50 500 1000 1500 age wage population regression function X 2 = + 1 X 2 1 =250 =500 Maria Casanova Lecture 6 2. The least squares assumptions Figure: Assumption 1 holds for this linear model 1 2 3 4 5 6 7 8 9 10 500 1000 1500 wage fitness (highest) (lowest) X 1 = = 1000 1 = 0 Maria Casanova Lecture 6 2. The least squares assumptions Figure: Assumption 1 holds for this linear model 1 2 3 4 5 6 7 8 9 10 500 1000 1500 fitness...
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This note was uploaded on 02/04/2010 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.

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slides_lecture6 - ECON 103, Lecture 6: The linear...

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