OHCh2 - Chapter 2: Ordinary Least Squares Revised on...

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Chapter 2: Ordinary Least Squares Revised on September 25, 2007
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1 Estimating Single-Independent-Variable Mod- els with OLS We now discuss how to estimate the unknown parameters & 0 and 1 . Estimating these two unknown parameters by choosing & 0 and 1 in Y i = ^ & 0 + ^ 1 X i + e i (1) We choose & 0 and 1 in such a way that the residual
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e i = Y i ^ Y i (2) Y i ( ^ & 0 + ^ 1 X i ) (3) is as "small" as possible under a certain criterion. Note that the residual, e i line. There are at least three di±erent criteria that one could use: (1) Minimizing the sum of the residuals : The problem of minimizing the small as we please if we are allowed to make the sum negative. (2) Minimizing the sum of absolute values of the residuals : This criterion is technically di²cult to use because the absolute value function is not
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This note was uploaded on 07/17/2008 for the course ECON 444 taught by Professor Ogaki during the Fall '07 term at Ohio State.

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OHCh2 - Chapter 2: Ordinary Least Squares Revised on...

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