Group least squares regression for linear models with strongly correlated predictor variables

@article{Tsao2018GroupLS,
  title={Group least squares regression for linear models with strongly correlated predictor variables},
  author={Min Tsao},
  journal={Annals of the Institute of Statistical Mathematics},
  year={2018},
  volume={75},
  pages={233-250},
  url={https://api.semanticscholar.org/CorpusID:237396158}
}
Traditionally, the main focus of the least squares regression is to study the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects. To resolve the multicollinearity issue without abandoning the least squares regression, for situations where predictor variables are in groups with strong within-group correlations but weak between-group correlations, we propose to study the effects of the groups with… 
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24 References

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