slides_Ch2_W[1]

Slides_Ch2_W[1]

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Unformatted text preview: ui and de…ne: ˆ ˆ TOTAL SUM OF SQUARES: measures the sample variation in the y 0 s n SST = ∑ (yi y )2 ¯ (2.33) i =1 Melissa Tartari (Yale) Econometrics 40 / 93 Algebraic Properties: Goodness of Fit Recall yi = yi + ui and de…ne: ˆ ˆ TOTAL SUM OF SQUARES: measures the sample variation in the y 0 s n SST = ∑ (yi y )2 ¯ (2.33) i =1 EXPLAINED SUM OF SQUARES: measures the sample variation in the y 0 s (why? y = y ) ˆ ¯ ˆ n SSE = ˆ ∑ (yi y )2 ¯ (2.34) i =1 Melissa Tartari (Yale) Econometrics 40 / 93 Algebraic Properties: Goodness of Fit Recall yi = yi + ui and de…ne: ˆ ˆ TOTAL SUM OF SQUARES: measures the sample variation in the y 0 s n SST = ∑ (yi y )2 ¯ (2.33) i =1 EXPLAINED SUM OF SQUARES: measures the sample variation in the y 0 s (why? y = y ) ˆ ¯ ˆ n SSE = ˆ ∑ (yi y )2 ¯ (2.34) i =1 RESIDUAL SUM OF SQUARES: measures the sample variation in the u 0 s (why? u = 0) ˆ ˆ n SSR = ˆ ∑ ui2 (2.35) i =1 Melissa Tartari (Yale) Econometrics 40 / 93 Algebraic Properties: Goodness of Fit Observe that by construction SST = SSE + SSR Melissa Tartari (Yale) Econometrics (2.36) 41 / 93 Algebraic Properties: Goodness of Fit Observe that by construction SST = SSE + SSR (2.36) With these new statistics we can tackle to the following issues: Melissa Tartari (Yale) Econometrics 41 / 93 Algebraic Properties: Goodness of Fit Observe that by construction SST = SSE + SSR (2.36) With these new statistics we can tackle to the following issues: How can we summarize how well X explains Y ? Melissa Tartari (Yale) Econometrics 41 / 93 Algebraic Properties: Goodness of Fit Observe that by construction SST = SSE + SSR (2.36) With these new statistics we can tackle to the following issues: How can we summarize how well X explains Y ? How well does the OLS line …t the data? Melissa Tartari (Yale) Econometrics 41 / 93 Algebraic Properties: Goodness of Fit Observe that by construction SST = SSE + SSR (2.36) With these new statistics we can tackle to the following issues: How can we summarize how well X explains Y ? How well does the OLS line …...
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This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

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