# I. Goodness of Fit II. Unbiasedness (2 pages)

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## I. Goodness of Fit II. Unbiasedness

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I. Goodness of Fit II. Unbiasedness

- Lecture number:
- 11
- Pages:
- 2
- Type:
- Lecture Note
- School:
- Cornell University
- Course:
- Econ 3120 - Applied Econometrics
- Edition:
- 1

**Unformatted text preview: **

Econ 3120 1st Edition Lecture 11 Outline of Current Lecture I Regression Current Lecture I II Goodness of Fit Unbiasedness Goodness of fit First recall from above that y can be decomposed as follows yi y i u i 8In order to analyze goodness of fit how well the regression fits the data it is useful to define the following total sum of squares SST yi y 2 explained sum of squares SSE y i y 2 residual sum of squares SSR u 2 i Note that the the explained sum of squares is sometimes called the regression sum of squares or model sum of squares The total sum of squares can be decomposed into the explained plus the residual sum of squares SST SSE SSR 4 3 R squared The R squared of a regression gives us a measure of goodness of fit It is defined as R 2 SSE SST 1 SSR SST In words this is the fraction of the variation in y that is explained by x Note that the definition implies that 0 R 2 1 Note that in economics it is not uncommon to have an R squared close to 0 In our regression of wages on schooling the R squared equals 0 140 While this implies that variation in schooling does not explain much of the variation in wages it does not necessarily mean that we have not done a good job estimating the relationship between schooling and earnings 95 Units of Measurement When running regressions sometimes it s convenient to change the units of measurement so that the regression estimates are easy to read Consider the following example Ashraf Berry and Shapiro 2010 analyze the results of a field experiment in Zambia which estimated the demand for bottles of water purification solution among a sample of 1004 urban households Bottles were offered for sale to individual households at prices between 300 and 800 Zambian Kwacha 3600 Kwacha 1 The authors estimate the following demand equation purchasei 0 1 pricei ui where purchasei is a variable which equals 1 if the household purchased the bottle and 0 otherwise and pricei is the price in Kwacha 1 Estimation of this equation yields the

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