Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Case influence diagnostics for the significance of the linear regression model

  • Bae, Whasoo (Department of Statistics, Inje University) ;
  • Noh, Soyoung (Department of Statistics, Pusan National University) ;
  • Kim, Choongrak (Department of Statistics, Pusan National University)
  • Received : 2016.12.16
  • Accepted : 2017.01.20
  • Published : 2017.03.31
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Abstract

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination $R^2$ and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in $R^2$ and F-statistic.

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References

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