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# P2 - Econ 444 Elementary Econometrics(Fall 2007 SUMMARY of...

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Econ 444 Elementary Econometrics (Fall 2007) SUMMARY of CHAPTER 2 and HOMEWORK EXERCISE: 2 Due at the beginning of class on Monday, October 8 1 KEY TERMS, CONCEPTS, and Formulas The least squares principle, Ordinary Least Squares (OLS), Multiple Regre- sion The Formulas for OLS estimates for K=1: ^ 1 = [( P N i =1 ( X i X )) ± ( Y i Y )] P N i =1 ( X i X ) 2 : (1) ^ & 0 = Y ^ 1 X; (2) Two features of the OLS estimators. (1) The estimated regression obtained by the OLS passes through the sample mean values of X and Y : Y = ^ & 0 + ^ 1 ± X: (3) (2) The sample mean value of the residuals is always equal to zero (except for the rounding error): e = 1 N N X i =1 e i = 0 : (4) The total sum of squares , or TSS, is TSS = N X i =1 ( Y i Y ) 2 : (5) The explained sum of squares , or ESS, is 1

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ESS = N X i =1 ( ^ Y i Y ) 2 : (6) The residual sum of squares, or RSS, is RSS = N X i =1 e 2 i : (7) TSS = ESS + RSS: (8) R 2 , the coe¢ cient of determination, by
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P2 - Econ 444 Elementary Econometrics(Fall 2007 SUMMARY of...

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