OHCh2-B - Chapter 2: Ordinary Least Squares Lecture 2...

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Chapter 2: Ordinary Least Squares Lecture 2 Revised on October 12, 2007
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1 Multiple Regression 1.1 The Population Regression When we study demand for a good from households, we often consider income of each household in addition to the price of the good. If there are additional independent variables, the population regression is E ( Y i j X 1 i ;:::;X Ki ) = & 0 + 1 X 1 i + ::: + K X Ki (1)
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For example, for K = 2, E ( Y i j X 1 i ;X 2 i ) = & 0 + 1 X 1 i + 2 X 2 i (2) 1 2 K are called . Let ± i = Y i E ( Y i j X 1 i ;:::X Ki ) be the stochastic error term. Then Y i = & 0 + 1 X 1 i + ::: + K X Ki + ± i (3) where the systematic component is & 0 + 1 X 1 i + ::: + K X Ki , which is E ( Y i j X 1 i ;:::;X Ki ), and the nonsystematic component is ± i .
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1.2 In Equation (2), 1 measures the change in the expected value of Y per unit change in X 1 , holding the value of X 2 constant. Likewise, 2 measures the change in the expected value of Y per unit change in X 2 , holding the value of X 1 constant. 1.3
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OHCh2-B - Chapter 2: Ordinary Least Squares Lecture 2...

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