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Coefficient of determination in some atypical situations: use in chemical correlation analysis
Author(s) -
Exner Otto,
Zvára Karel
Publication year - 1999
Publication title -
journal of physical organic chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 66
eISSN - 1099-1395
pISSN - 0894-3230
DOI - 10.1002/(sici)1099-1395(199902)12:2<151::aid-poc108>3.0.co;2-1
Subject(s) - linear regression , correlation coefficient , chemistry , interpretation (philosophy) , regression analysis , statistics , variable (mathematics) , correlation , mathematics , statistical physics , mathematical analysis , physics , computer science , geometry , programming language
Abstract The popular statistics used in correlation analysis, the correlation coefficient R and coefficient of determination R 2 , belong to the model of common linear regression with an exact explanatory variable and freely fitted intercept. When they are used in other models, the common equation must be modified and the interpretation revised. The resulting equations are discussed for the model with a fixed intercept. For the models with errors in either variable and with both modifications, new equations are suggested. Under these conditions, R may be defined differently, always in at least two ways; the different interpretations are discussed. Some properties of these definitions are shown, particularly the sensitivity to coordinate transformations. These properties and interpretations differ from those of R in the common linear regression, hence the values in different models must not be directly compared. Applications in chemistry and some cases of misuse in the literature are mentioned. Copyright © 1999 John Wiley & Sons, Ltd.