Weighted Least Squares Regression, 2013 Edition

by G. David Garson

WEIGHTED LEAST SQUARES REGRESSIONA graduate-level introduction and illustrated tutorial on weighted least squares regression (WLS) using SPSS, SAS, or Stata. WLS addresses the heteroscedasticity problem in OLS. In the face of heteroscedasticity, ordinary regression computes erroneous standard errors. This in turn makes significance tests incorrect.New in the 2013 twice as much depth (now 54 pp. compared to 19 in the 2012 edition)Covers SPSS, SAS, and StataDiscussion of a wide variety of weighting functions.Explains why robust standard errors do not substitute for WLS25 new illustrationsBelow is the unformatted table of contents.WEIGHTED LEAST SQUARESTable of ContentsOverview of WLS5What the researcher can expect if WLS regression is needed6Are robust standard errors a substitute for WLS?6Weighting with replicates7Weight estimation functions8Data example9Key Terms and Concepts9The homoscedasticity assumption in regression9Weighted cases11WLS in SPSS11SPSS overview11Testing for heteroscedasticity in SPSS11The graphical method11Statistical tests for heteroscedasticity12Park test13Breusch-Pagan test15White's test16Goldfeld-Quandt test16Glejser test17Weighting cases in SPSS17Weight estimation Weighting with powers17Weight estimation The log-likelihood values table19Output from SPSS Weight Estimation21SPSS OLS regression on weighted cases23SPSS input23SPSS output24WLS in SAS28Overview28SAS input29SAS output34WLS in Stata39Stata overview39Stata input39Stata output42Assumptions45Proper specification45Proper weighting46Data level46Multivariate normality46Linearity46Independence46Predictable variance47Frequently Asked Questions47Is WLS regression something that could be used with regression models other than OLS?47What is SPSS syntax for WLS?47How can one get OLS regression with robust standard errors in SAS?48How does PROC ROBUSTREG in SAS work?48Heteroskedasticity or heteroscedasticity?51 54

58 pages, Kindle Edition

First published December 4, 2013