Influential Observations in Linear Regression

Cook, R. Dennis

doi:10.2307/2286747

Cited by 510 publications

(561 citation statements)

References 3 publications

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“…Highlighted cases had Cook's distance > min(0.5, 2p/n). See Cook (1977). Figure 3 shows the DD plot of the residual vectors.…”

Section: Resultsmentioning

confidence: 99%

Visualizing and Testing the Multivariate Linear Regression Model

Olive¹,

Watagoda²,

Don³

2015

IJSP

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Recent results make the multivariate linear regression model much easier to use. This model has m ≥ 2 response variables. Results by Kakizawa (2009) and Su and Cook (2012) can be used to explain the large sample theory of the least squares estimator and of the widely used Wilks' Λ, Pillai's trace, and Hotelling Lawley trace test statistics. Kakizawa (2009) shows that these statistics have the same limiting distribution. This paper reviews these results and gives two theorems to show that the Hotelling Lawley test generalizes the usual partial F test for m = 1 response variable to m ≥ 1 response variables. Plots for visualizing the model are also given, and can be used to check goodness and lack of fit, to check for outliers and influential cases, and to check whether the error distribution is multivariate normal or from some other elliptically contoured distribution.

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“…Highlighted cases had Cook's distance > min(0.5, 2p/n). See Cook (1977). Figure 3 shows the DD plot of the residual vectors.…”

Section: Resultsmentioning

confidence: 99%

Visualizing and Testing the Multivariate Linear Regression Model

Olive¹,

Watagoda²,

Don³

2015

IJSP

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“…Raw microarray data have been deposited with Gene Expression Omnibus under accession number: GSE47874 23a. After QC and removal of outliers (N=2 with Cook's distance >0.5),24 baseline microarray data were available for 49 participants.…”

Section: Methodsmentioning

confidence: 99%

Genomic and transcriptomic predictors of triglyceride response to regular exercise

et al. 2015

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Aim We performed genome-wide and transcriptome-wide profiling to identify genes and single nucleotide polymorphisms (SNPs) associated with the response of triglycerides (TG) to exercise training. Methods Plasma TG levels were measured before and after a 20-week endurance training programme in 478 white participants from the HERITAGE Family Study. Illumina HumanCNV370-Quad v3.0 BeadChips were genotyped using the Illumina BeadStation 500GX platform. Affymetrix HG-U133+2 arrays were used to quantitate gene expression levels from baseline muscle biopsies of a subset of participants (N=52). Genome-wide association study (GWAS) analysis was performed using MERLIN, while transcriptomic predictor models were developed using the R-package GALGO. Results The GWAS results showed that eight SNPs were associated with TG training-response (ΔTG) at p<9.9×10−6, while another 31 SNPs showed p values <1×10−4. In multivariate regression models, the top 10 SNPs explained 32.0% of the variance in ΔTG, while conditional heritability analysis showed that four SNPs statistically accounted for all of the heritability of ΔTG. A molecular signature based on the baseline expression of 11 genes predicted 27% of ΔTG in HERITAGE, which was validated in an independent study. A composite SNP score based on the top four SNPs, each from the genomic and transcriptomic analyses, was the strongest predictor of ΔTG (R2=0.14, p=3.0×10−68). Conclusions Our results indicate that skeletal muscle transcript abundance at 11 genes and SNPs at a number of loci contribute to TG response to exercise training. Combining data from genomics and transcriptomics analyses identified a SNP-based gene signature that should be further tested in independent samples.

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“…To identify these data points, which are observations with large residuals that affect the dependent variable value in an unusual form, we first calculated the leverage by standardizing the predictor variable to a mean equal to zero and a standard deviation equal to one. Given that the influence of an observation is dependent on how much the predicted scores for other observations would differ if the observation in question was not included, we used a Cook's D to calculate this influence, as those points with the largest influence produce the largest change in the equation of the regression line (Altman and Krzywinski, 2016;Cook, 1979). In particular, to identify potential outperformers, we applied the following expression for country i in each of the considered regressions:…”

Section: Identification Of Outliersmentioning

confidence: 99%

Trade, Global Value Chains and Upgrading: What, When and How?

Sampath¹,

Vallejo

2018

Eur J Dev Res

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This paper explains how successful innovation systems interact with trade and global value chains (GVC) participation to foster learning and technological upgrading. It conducts an empirical investigation of 74 developing countries for 3 years, 2000, 2005 and 2010, to show that, while some countries manage to trade and export across a large number of technological export categories, many remain embedded in the export of low technology goods with little movement technologically. The analysis looks at why this is the case and what factors account for how firms are able to leverage trade to learn and upgrade in some instances, but not all. The results show that the ability to technologically diversify across export categories is linked to stronger innovation systems, as measured by national capability indicators, such as public R&D investments, scientific publications, intellectual property payments and patents by residents. The results also confirm the rise of several outperforming countries, the emerging economies. We conclude that, in successful, outperforming countries, firms rely on several attributes of the innovation system to leverage knowledge flows within and outside of GVCs to build export capacity and diversify horizontally into new GVCs.Cet article explique comment les systèmes d'innovation efficaces interagissent avec les activités liées au commerce et à la chaîne de valeur mondiale (CVM) pour favoriser l'apprentissage et la modernisation technologique. Il décrit une enquête empirique sur 74 pays en développement sur trois années, 2000, 2005 et 2010, pour montrer que, si certains pays parviennent à commercer et à exporter un large spectre de technologies, beaucoup restent cantonnés à l'exportation de produits de basse technologie et avec peu de changements technologiques. L'article analyse les raisons derrière cela et les facteurs qui expliquent pourquoi, dans certains cas mais pas tous, les entreprises sont en mesure de tirer parti du commerce pour apprendre et se mettre à niveau sur le plan technologique. Les résultats montrent que la capacité à diversifier les catégories de produits technologiques voués à l'exportation est liée à des systèmes d'innovation plus forts, comme mesurés par les indicateurs nationaux de capacité tels que les investissements R&D publics, les publications scientifiques, les paiements et brevets de propriété intellectuelle déposés par les résidents. Les résultats confirment également l'essor de plusieurs pays surperformants que sont les économies émergentes. Nous concluons que dans les pays qui réussissent et qui sont surperformants, les entreprises s'appuient sur plusieurs attributs du système d'innovation pour tirer parti des flux de connaissances à l'intérieur et à l'extérieur des CVM pour renforcer la capacité d'exportation et se diversifier horizontalement dans de nouvelles CVM.

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Influential Observations in Linear Regression

Cited by 510 publications

References 3 publications

Visualizing and Testing the Multivariate Linear Regression Model

Visualizing and Testing the Multivariate Linear Regression Model

Genomic and transcriptomic predictors of triglyceride response to regular exercise

Trade, Global Value Chains and Upgrading: What, When and How?

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