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Estimation of influential points in any data set from coefficient of determination and its leave-one-out cross-validated counterpart

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Abstract

Coefficient of determination (R 2) and its leave-one-out cross-validated analogue (denoted by Q 2 or R 2cv ) are the most frequantly published values to characterize the predictive performance of models. In this article we use R 2 and Q 2 in a reversed aspect to determine uncommon points, i.e. influential points in any data sets. The term (1 − Q 2)/(1 − R 2) corresponds to the ratio of predictive residual sum of squares and the residual sum of squares. The ratio correlates to the number of influential points in experimental and random data sets. We propose an (approximate) F test on (1 − Q 2)/(1 − R 2) term to quickly pre-estimate the presence of influential points in training sets of models. The test is founded upon the routinely calculated Q 2 and R 2 values and warns the model builders to verify the training set, to perform influence analysis or even to change to robust modeling.

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Authors and Affiliations

  1. Institute of Chemistry, Loránd Eötvös University, Pázmány Sétány 1/a, Budapest, 1117, Hungary

    Gergely Tóth & Zsolt Bodai

  2. Institute of Materials and Environmental Chemistry, Research Centre of Natural Sciences, Hungarian Academy of Sciences, Pusztaszeri út 59-67, Budapest, 1025, Hungary

    Károly Héberger

Authors
  1. Gergely Tóth
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  2. Zsolt Bodai
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  3. Károly Héberger
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Correspondence to Károly Héberger.

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Tóth, G., Bodai, Z. & Héberger, K. Estimation of influential points in any data set from coefficient of determination and its leave-one-out cross-validated counterpart. J Comput Aided Mol Des 27, 837–844 (2013). https://doi.org/10.1007/s10822-013-9680-4

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  • DOI: https://doi.org/10.1007/s10822-013-9680-4

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