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WEIGHTED LEAST SQUARES REGRESSION

A 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.

Why we think it's important: Heteroscedasticity is a common regression problem which causes significance tests to be in error. Moreover, contrary to widely held belief, regression with robust standard errors does not substitute for WLS, which is rarely covered in general texts on multivariate analysis.

New in the 2013 edition:

Over twice as much depth (now 54 pp. compared to 19 in the 2012 edition)

• Covers SPSS, SAS, and Stata
• Discussion of a wide variety of weighting functions.
• Explains why robust standard errors do not substitute for WLS
• 25 new illustrations

The full content is now available from Statistical Associates Publishers. Click here.

```WEIGHTED LEAST SQUARES
Overview of WLS	5
What the researcher can expect if WLS regression is needed	6
Are robust standard errors a substitute for WLS?	6
Weighting with replicates	7
Weight estimation functions	8
Data example	9
Key Terms and Concepts	9
The homoscedasticity assumption in regression	9
Weighted cases	11
WLS in SPSS	11
SPSS overview	11
Testing for heteroscedasticity in SPSS	11
The graphical method	11
Statistical tests for heteroscedasticity	12
Park test	13
Breusch-Pagan test	15
White's test	16
Goldfeld-Quandt test	16
Glejser test	17
Weighting cases in SPSS	17
Weight estimation input: Weighting with powers	17
Weight estimation output: The log-likelihood values table	19
Output from SPSS Weight Estimation	21
SPSS OLS regression on weighted cases	23
SPSS input	23
SPSS output	24
WLS in SAS	28
Overview	28
SAS input	29
SAS output	34
OLS output	34
WLS output	38
WLS in Stata	39
Stata overview	39
Stata input	39
Stata output	42
Unweighted linear regression	42
Weighted least squares regression	44
Assumptions	45
Proper specification	45
Proper weighting	46
Data level	46
Multivariate normality	46
Linearity	46
Independence	46
Predictable variance	47