Heteroskedasticity WLS Lecture

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Heteroskedasticity 1/55 Heteroskedasticity in Regression Paul E. Johnson 1 2 1 Department of Political Science 2 Center for Research Methods and Data Analysis, University of Kansas 2014  Heteroskedasticity 2/55Introduction Outline 1  Introduction 2  Fix #1: Robust Standard Errors 3  Weighted Least SquaresCombine Subsets of a SampleRandom coeﬃcient modelAggregate Data 4  Testing for heteroskedasticityCategorical HeteroskedasticityChecking for Continuous HeteroskedasticityToward a General Test for Heteroskedasticity 5  Appendix: Robust Variance Estimator Derivation 6  Practice Problems  Heteroskedasticity 3/55Introduction Remember the Theory Linear Model y  i   =  β  0  +  β  1 x  1 i   +  e  i  About the error term, we assumed, for all  i  , E  ( e  i  ) = 0 for all i Var  ( e  i  ) =  E  [( e  i  − E  ( e  i  )) 2 ] =  σ 2 (Homoskedasticity).There is no  i   subscript on  σ 2 . It is the same for all rows. Heteroskedasticity (or heteroscedasticity): the assumption of homogeneous variance is violated.  Heteroskedasticity 4/55Introduction Homoskedasticity means Var  ( e  ) =  σ 2 e   0 0 0 00  σ 2 e   0 0 00 0  σ 2 e   0 00 0 0 ... 00 0 0 0  σ 2 e  

Apr 16, 2018

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