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. 2017 Dec 11;17:246. doi: 10.1186/s12909-017-1070-5

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© The Author(s). 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Fig. 1 — a Scattergram of X₁ and X₂. 20% of 1000 applicants are selected by the sum of X₁ and X₂; the circular cloud representing all applicants is divided by a diagonal line that separates the top right area from the bottom left area. b This generates a negative correlation between X₁ and X₂ in the incumbents $(r_{x_{1} x_{2} ∣ i} = - 0.71)$ . Residuals of X₁ after the linear effect of X₂ is removed. They are expressed as deviations from the regression line: The residuum of X₁ when the influence of X₂ is removed is the observed X₁ value minus the expected value of the regression X₁ on X₂