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Unformatted text preview: y = b + b 1 x + u The Simple Regression Model (cont.) 2 OUTLINE 1. Algebraic Properties of OLS 2. Goodness of Fit 3. Statistical properties of OLS 3 Property 1: The sum of the OLS residuals is zero. Thus, the sample average of the OLS residuals is zero as well. Property 2: The sample covariance between the regressors and the OLS residuals is zero. Property 3: The OLS regression line always goes through the mean of the sample. 1. Algebraic properties of OLS 4 x y u x n u u n i i i n i i n i i 1 1 1 1 ) 3 ( ) 2 ( thus, and ) 1 ( b b 1. Algebraic properties of OLS Question Example: Wage equation wage = b 0 + b 1 educ + u Given a sample of data, you estimate the above model by OLS i.e. run the regression of hourly wages on years of education. You get the following estimates: ?? = . ? + . ???? Youve been given that the sample average of educ is 12.56. What is the sample average of hourly wages? Question Example: Wage equation wage = b 0 + b 1 educ + u Given a sample of data, you estimate the above model by OLS i.e. run the regression of hourly wages on years of education. You get the following estimates: ?? = . ? + . ???? Youve been given that the sample average of educ is 12.56 years What is the sample average of hourly wages? Make use of the third algebraic property. ?? = . ? + . ?? . ?? = ?. ?. 7 We can decompose each observation of y in a explained part and an unexplained or residual part . 2. GOODNESS OF FIT SSR SSE SST : that show to p ossible is It (SSR) squares of sum residual the is (SSE) squares of sum exp lained the is (SST ) squares of sum total the is : follow ing the define then W e 2 2 2 i i i i i i u y y y y u y y 8 Proof that SST = SSE + SSR that know w e and SSE 2 SSR 2 2 2 2 2 2 y y u y y u y y y y u u y y u y y y y y y i i i i i i i i i i i i i i 9 How do we think about how well our sample regression line fits our sample data?...
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This note was uploaded on 02/29/2012 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Spring '10 term at Rutgers.
 Spring '10
 Otusbo
 Econometrics

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