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Unformatted text preview: Weighted Least Squares Regression A technique for correcting the problem of heteroskedasticity by log likelihood estimation of a weight that adjusts the errors of prediction Weighted LeastSquares Regression: Charles M. Friel Ph.D., Criminal Justice Center, Sam Houston State University Key Concepts ***** Weighted LeastSquares Regression OLS Parameter estimates as: Unbiased Efficient BLUE Theoretical Sampling distribution of b Standard error of b Relationship between the standard error of b and: The variance of X The residual sum of squares The sample size GaussMarkov Theorem Assumptions about the errors (e) in regression analysis and the consequences of their violation: e is uncorrelated with X e has the same variance across all levels of X The values of e are independent of each other e is normally distributed The concepts of homoskedasticity and heteroskedasticity of the error distributions The concept of autocorrelation or serial correlation Spurious relationships Collinear relationships Intervening relationships Techniques for identifying heteroskedasticity Graphic Statistical White’s Test for heteroskedasticity Rezidualizing a variable Techniques for identifying WLS weights Theory, the literature, or prior experience Regression of e 2 on X and transformation Loglikelihood estimation of w i SPSS weight estimation procedure SPSS WLS procedure Weighted Leastsquares Regression: Charles M. Friel Ph.D., Criminal Justice Center, Sam Houston State University 2 Overview Theoretical sampling distribution of b Assumptions about errors in regression Identifying heteroskedasticity The concept of weighted leastsquares regression Methods for estimating weights Regressing e i 2 on X Loglikelihood estimation of weights Using WLS>> command in SPSS Weighted Leastsquares Regression: Charles M. Friel Ph.D., Criminal Justice Center, Sam Houston State University 3 References White, Halbert (1980) A heteroskedasticityconsistent covariance matrix estimator and a direct test for heteroskedasticity . Econometrica 48:817838. Graybill, Fraklin A. and Iyer, Hariharan K. (1994) Regression Analysis: Concepts and Applications. Duxbury Press 571592. Freund, Rudolf J. and Wilson, William J. (1998) Regression Analysis: Statistical Modeling of a Response Variable. Academic Press 378382. McClendon, McKee J. (1994) Multiple Regression and Causal Analysis. F. E. Peacock Publishers, Inc. 138146, 174181, 189197. Weighted Leastsquares Regression: Charles M. Friel Ph.D., Criminal Justice Center, Sam Houston State University 4 Violation of OLS Regression Assumptions Y = a + b 1 X 1 + b 2 X 2 + … + b k X k OLS regression makes various assumptions about the errors that result from a regression model....
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This note was uploaded on 02/15/2012 for the course GEO 4167 taught by Professor Staff during the Spring '12 term at University of Florida.
 Spring '12
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