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Unformatted text preview: Lecture 5 : Goodness of fit, Classical Assumptions Econ 444, Winter 2010 Jan 24, 2010 1. Describing the Overall fit of the Estimated Model As a measure of "goodness of fit" we have the coefficient of determination , denoted by the symbol R 2 (read as r squared). To define this measure we need to develop some measures of variation, namely, Total, Explained, and Residual Sums of Squares. 1 The total sum of squares , or TSS, is TSS = N X i = 1 ( Y i Y ) 2 . (1) This is a measure of variation of the dependent variable, and becomes larger when an observed value of the dependent variable deviate more from its sample average. 2 The explained sum of squares , or ESS, is ESS = N X i = 1 ( ˆ Y i Y ) 2 . (2) This is a measure of variation of the fitted value, and becomes larger when the fitted value for i deviates more from the sample average of the dependent variable. 3 The residual sum of squares, or RSS, is RSS = N X i = 1 e 2 i . (3) This is a measure of variation of the residual, and becomes larger when the absolute value of the residual for i is larger. The relationship between TSS, ESS, and RSS is : TSS = ESS + RSS . (4) Equation ( ?? ) decomposes the TSS into two components. One is ESS, and the other is RSS. Now we can define R 2 or the Coefficient of Determination by R 2 = ESS TSS (5) Note that 0 ≤ R 2 ≤ 1, and that an alternative formula to compute R 2 is R 2 = 1 RSS TSS (6) A value of R 2 close to one shows an excellent overall fit, whereas a value near zero shows a bad overall fit....
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 Winter '07
 OGAKI
 Econometrics, Regression Analysis, Yi, ols estimator, classical assumptions

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