# Questions tagged [wls]

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### Very basic questions about choosing weights for WLS

Hi all – very new to stats and ML here (though with plenty of math experience – I’m not a student looking for homework help, I’m 58, know plenty of math, and am looking to expand my skills).  I ...
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### Why does systemfit yield different results for OLS and WLS under cross-equation restrictions?

I am following up on the question "Why does systemfit yield identical results for OLS and WLS?". It deals with estimating a system of linear equations ...
• 68.6k
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### Why does systemfit yield identical results for OLS and WLS?

I am estimating a system of seemingly unrelated regressions (SUR) using the systemfit package in R. Each of the equations has one unique regressor and one common ...
• 68.6k
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### How critical/serious is the heteroscedasticity in my data (Breusch-Pagan test significant at p=.03)?

edit below I am doing this analysis for the first time. How concerned should I be about heteroscedasticity in my data? Here's the scatterplot of predicted values vs residuals: The Breusch-Pagan test ...
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28 views

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### Comparing non-nested models estimated by Weighted Least Squares

It's very common for social scientists to have binary or ordinal indicators (e.g., yes/no interview items or likert-rated questionnaire items). It's also very common for them to model their ordered/...
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1 vote
756 views

### FA estimation (GLS/WLS/DWLS/ULS) and robustness of these estimators

I have cross-sectional survey data, with over 4000 observations on 41 variables, and there are no missing values. Variables are not normally distributed and assumptions of multinormal distribution are ...
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556 views

### Quality of weighted least square fit

I fitted a linear regression with heteroscedescity using weighted least square method. How do I evaluate the quality of my fitting? I’m thinking by the p-value of slope/intercept. Or maybe because I ...
• 155
For OLS, $\hat{\beta} = (X'X)^{-1}X'y$, and $\text{var}(\hat{\beta}) = (X'X)^{-1} X' \sigma^2 I X (X'X)^{-1}$. I can reproduce these "by hand". For WLS, with heteroskedastic errors and weights in ...