Regression Analysis by Example

Chatterjee, Samprit; Hadi, Ali S.

doi:10.1002/0470055464

Cited by 1,699 publications

(1,684 citation statements)

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“…13, 14 For readers with mathematical minds, technical explanations of the problems of collinearity and multicollinearity can be found in our previous article 15 and advanced statistical textbooks. 7,8,10,11,16 Collinearity Consider a multiple regression model with two covariates:…”

Section: N B R I E Fmentioning

confidence: 99%

“…The variance inflation factor (VIF), defined as VIF=1/(1-R 2 i) where R 2 i is the R 2 for a covariate xi regressed on the remaining covariates in a auxiliary regression, is the most commonly used EDUCATION regression diagnostic for multicollinearity within standard statistical software. [7][8][9][10][11] Another diagnostic tool for multicollinearity is the condition index, which is more complicated but provides very similar information as the VIF. 8,14 Detailed explanations of these diagnostics can be found in the cited references.…”

Section: Diagnosis Of Multicollinearitymentioning

confidence: 99%

“…8,14 Detailed explanations of these diagnostics can be found in the cited references. [7][8][9][10][11] In general, standard errors of regression coefficients are inflated when the VIF is large (eg when VIF>10, multicollinearity is usually considered a problem, though this is an arbitrary threshold).…”

Section: Diagnosis Of Multicollinearitymentioning

confidence: 99%

“…Moreover, even when there is a problem of multicollinearity, the collinear covariates may remain statistically significant, though the sign of regression coefficient might be contrary to expectationthis is another indication of potential problems due to multicollinearity. [7][8][9][10] In the next sections, we use three examples within dental research to illustrate how to detect the problem of collinearity. It should be noted that these examples were selected as they exhibit good quality in the reporting of their regression analyses, thereby providing sufficient information to the reader to evaluate whether or not collinearity is a potential problem.…”

Section: Diagnosis Of Multicollinearitymentioning

confidence: 99%

“…6 Most textbooks emphasise that there should be no significant associations between covariates, as this gives rise to the problem known as collinearity. [6][7][8][9][10][11] When there are more than two covariates that are highly correlated, this is multicollinearity. Collinearity and multicollinearity can seriously distort the interpretation of a model.…”

Section: Introductionmentioning

confidence: 99%

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Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

et al. 2005

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Multivariable analysis is a widely used statistical methodology for investigating associations amongst clinical variables. However, the problems of collinearity and multicollinearity, which can give rise to spurious results, have in the past frequently been disregarded in dental research. This article illustrates and explains the problems which may be encountered, in the hope of increasing awareness and understanding of these issues, thereby improving the quality of the statistical analyses undertaken in dental research. Three examples from different clinical dental specialities are used to demonstrate how to diagnose the problem of collinearity/multicollinearity in multiple regression analyses and to illustrate how collinearity/multicollinearity can seriously distort the model development process. Lack of awareness of these problems can give rise to misleading results and erroneous interpretations. Multivariable analysis is a useful tool for dental research, though only if its users thoroughly understand the assumptions and limitations of these methods. It would benefit evidencebased dentistry enormously if researchers were more aware of both the complexities involved in multiple regression when using these methods and of the need for expert statistical consultation in developing study design and selecting appropriate statistical methodologies.

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Section: N B R I E Fmentioning

confidence: 99%

Section: Diagnosis Of Multicollinearitymentioning

confidence: 99%

Section: Diagnosis Of Multicollinearitymentioning

confidence: 99%

Section: Diagnosis Of Multicollinearitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

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The Cumulative Effect of Unemployment on Risks for Acute Myocardial Infarction

Dupre¹,

George²,

Liu³

et al. 2012

Arch Intern Med

153

101

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Prediction of relativistic electron flux at geostationary orbit following storms: Multiple regression analysis

et al. 2014

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Many solar wind and magnetosphere parameters correlate with relativistic electron flux following storms. These include relativistic electron flux before the storm; seed electron flux; solar wind velocity and number density (and their variation); interplanetary magnetic field B z , AE and Kp indices; and ultra low frequency (ULF) and very low frequency (VLF) wave power. However, as all these variables are intercorrelated, we use multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Using 219 storms (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002), we obtained hourly averaged electron fluxes for outer radiation belt relativistic electrons (>1.5 MeV) and seed electrons (100 keV) from Los Alamos National Laboratory spacecraft (geosynchronous orbit). For each storm, we found the log 10 maximum relativistic electron flux 48-120 h after the end of the main phase of each storm. Each predictor variable was averaged over the 12 h before the storm, the main phase, and the 48 h following minimum Dst. High levels of flux following storms are best modeled by a set of variables. In decreasing influence, ULF, seed electron flux, Vsw and its variation, and after-storm B z were the most significant explanatory variables. Kp can be added to the model, but it adds no further explanatory power. Although we included ground-based VLF power from Halley, Antarctica, it shows little predictive ability. We produced predictive models using the coefficients from the regression models and assessed their effectiveness in predicting novel observations. The correlation between observed values and those predicted by these empirical models ranged from 0.645 to 0.795.

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Regression Analysis by Example

Cited by 1,699 publications

References 0 publications

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

The Cumulative Effect of Unemployment on Risks for Acute Myocardial Infarction

Prediction of relativistic electron flux at geostationary orbit following storms: Multiple regression analysis

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