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Regression Residuals (regression + residual)
Selected AbstractsRegression residuals and test statistics: Assessing naive outlier deletionTHE CANADIAN JOURNAL OF STATISTICS, Issue 2 2000Debbie J. Dupuis Abstract The authors derive the joint distributions of a studentized deleted residual and various regression quantities, calculated with all the data or with one case deleted. They show that the correlation between the studentized deleted residual and the deleted test statistic has an interesting interpretation in terms of well-known regression quantities. These results allow them to examine the effect of applying some naive outlier deletion methods before making inferences about a regression parameter. Les auteurs déterminent la loi conjointe d'un résidu studentisé retranché et de certaines variables classiques en régression, calculées avec ou sans l'observation retranchée. IIs montrent que la corrélation entre le résidu studentisé retranché et la statistique de test obtenue sans cette observation possède une interprétation intéressante en fonction de statistiques bien connues. Ces résultats leur permettent d'étudier comment l'application de certaines techniques naïves de détection de valeurs aberrantes peut affecter l'inférence concernant un paramètre de régression. [source] The development of a new set of long-term climate averages for the UKINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 8 2005Matthew Perry Abstract Monthly and annual long-term average datasets of 13 climate variables are generated for the periods 1961,90 and 1971,2000 using a consistent analysis method. Values are produced for each station in the Met Office's observing network and for a rectangular grid of points covering the UK at a horizontal spacing of 1 km. The variables covered are mean, maximum, minimum, grass minimum and soil temperature, days of air and ground frost, precipitation, days with rain exceeding 0.2 and 1 mm, sunshine, and days with thunder and snow cover. Gaps in the monthly station data are filled with estimates obtained via regression relationships with a number of well-correlated neighbours, and long-term averages are then calculated for each site. Gridded datasets are created by inverse-distance-weighted interpolation of regression residuals obtained from the station averages. This method does not work well for days of frost, thunder and snow, so an alternative approach is used. This involves first producing a grid of values for each month from the available station data. The gridded long-term average datasets are then obtained by averaging the monthly grids. The errors associated with each stage in the process are assessed, including verification of the gridding stage by leaving out a set of stations. The estimation of missing values allows a dense network of stations to be used, and this, along with the range of independent variables used in the regression, allows detailed and accurate climate datasets and maps to be produced. The datasets have a range of applications, and the maps are freely available through the Met Office Website. © Crown Copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd. [source] The generation of monthly gridded datasets for a range of climatic variables over the UKINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 8 2005Matthew Perry Abstract Monthly or annual 5 km × 5 km gridded datasets covering the UK are generated for the 1961,2000 period, for 36 climatic parameters. As well as the usual elements of temperature, rainfall, sunshine, cloud, wind speed, and pressure, derived temperature variables (such as growing-season length, heating degree days, and heat and cold wave durations) and further precipitation variables (such as rainfall intensity, maximum consecutive dry days, and days of snow, hail and thunder) are analysed. The analysis process uses geographical information system capabilities to combine multiple regression with inverse-distance-weighted interpolation. Geographic and topographic factors, such as easting and northing, terrain height and shape, and urban and coastal effects, are incorporated either through normalization with regard to the 1961,90 average climate, or as independent variables in the regression. Local variations are then incorporated through the spatial interpolation of regression residuals. For each of the climatic parameters, the choice of model is based on verification statistics produced by excluding a random set of stations from the analysis for a selection of months, and comparing the observed values with the estimated values at each point. This gives some insight into the significance, direction, and seasonality of factors affecting different climate elements. It also gives a measure of the accuracy of the method at predicting values between station locations. The datasets are being used for the verification of climate modelling scenarios and are available via the Internet. © Crown Copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd. [source] Scale and the Scale Effect in Market-based Accounting ResearchJOURNAL OF BUSINESS FINANCE & ACCOUNTING, Issue 1-2 2003Peter D. Easton The nature of the data we usually encounter in market-based accounting research is such that the results of the regressions of market capitalization on financial statement variables (referred to ,price-levels' regressions) are driven by a relatively small subset of the very largest firms in the sample. We refer to this overwhelming influence of the largest firms as the ,scale effect'. This effect is more than heteroscedasticity. It arises due to the non-linearity in the relation between market capitalization and the financial statement variables. We present the case that scale is market capitalization rather than a correlated omitted variable. Since scale is market capitalization, we advocate its use as a deflator in a regression estimated using weighted least squares. This regression overcomes the scale effect and the resultant regression residuals are more economically meaningful. Christie's (1987) depiction of scale is the same as ours but he advocates the use of the returns regression specification in order to avoid scale effects. We agree that returns regressions should be used unless the research question calls for a price-levels regression. [source] The detailed forms of the LMC Cepheid PL and PLC relationsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007C. Koen ABSTRACT Possible deviations from linearity of the Large Magellanic Cloud Cepheid period,luminosity (PL) and period,luminosity,colour (PLC) relations are investigated. Two data sets are studied, respectively from the Optical Gravitational Lensing Experiment (OGLE) and MACHO projects. A non-parametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for, then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These findings are confirmed by fitting ,Generalized Additive Models' (non-parametric regression functions) to the two data sets. Colour dependence is shown to be non-linear in both data sets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and the colour functions in the MACHO data. [source] The effects of socioeconomic status on endochondral and appositional bone growth, and acquisition of cortical bone in children from 19th century Birmingham, EnglandAMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY, Issue 3 2009Simon Mays Abstract Endochondral growth, appositional growth, and acquisition of cortical bone thickness in the femur are investigated in subadult skeletons (N = 43, dental age range birth to 12 years) from the 19th -century AD burial site of St. Martin's churchyard, Birmingham, England. Endochondral growth is monitored using diaphyseal femoral length. Appositional growth is monitored using radiographic midshaft mediolateral width and acquisition of cortical bone using combined mediolateral cortical thickness measured at the midshaft from radiographs. The methodology involves plotting these variables against dental age. Growth is compared in children of differing socioeconomic status. Higher and lower status individuals are identified in the assemblage by their burial in brick vaults in the case of the former and in earth-cut graves in the case of the latter. The relationships between bone dimensions and dental age are described using a polynomial regression procedure, and analysis of regression residuals is used to evaluate differences in bone dimension-for-dental age between the two status groups. Results show that lower socioeconomic status individuals had lower cortical thickness-for-dental age than those of higher status. This was interpreted as likely reflecting poorer nutrition in the children of lower socioeconomic backgrounds. There was no patterning with respect to socioeconomic status in femur diaphyseal length or midshaft width. The results support the idea that, for skeletal populations, growth in cortical thickness may be a more sensitive indicator of adverse conditions in childhood than growth in bone length or width. Am J Phys Anthropol, 2009. © 2009 Wiley-Liss, Inc. [source] On describing multivariate skewed distributions: A directional approachTHE CANADIAN JOURNAL OF STATISTICS, Issue 3 2006José T. A. S. Ferreira Abstract Most multivariate measures of skewness in the literature measure the overall skewness of a distribution. These measures were designed for testing the hypothesis of distributional symmetry; their relevance for describing skewed distributions is less obvious. In this article, the authors consider the problem of characterizing the skewness of multivariate distributions. They define directional skewness as the skewness along a direction and analyze two parametric classes of skewed distributions using measures based on directional skewness. The analysis brings further insight into the classes, allowing for a more informed selection of classes of distributions for particular applications. The authors use the concept of directional skewness twice in the context of Bayesian linear regression under skewed error: first in the elicitation of a prior on the parameters of the error distribution, and then in the analysis of the skewness of the posterior distribution of the regression residuals. Décrire I'asyrnétrie de lois rnultivariées: une approche directionnelle La plupart des mesures d'asymétrie multivariées existantes donnent une idée de l'asymétrie globale d'une loi à plusieurs dimensions. Ces mesures ont été conçues pour tester l'hypothèse de symétrie distributionnelle; leur pertinence en tant qu'outil de description de l'asymétrie est moins claire. Dans cet article, les auteurs cherchent à caractériser l'asymétrie de lois multivariées. Ils définissent une notion d'asymétrie propre à une direction et étudient deux classes paramétriques de lois asymétriques à l'aide de mesures fondées sur ce concept. Leur analyse fournit des renseignements utiles sur les propriétés de ces classes de lois, permettant ainsi un choix plus éclairé dans des applications spécifiques. Les auteurs font double emploi de leur concept d'asymétrie directionnelle dans un contexte de régression linéaire bayésien-ne: d'abord pour l'élicitation d'une loi a priori sur les paramètres de la loi du terme d'erreur, puis pour l'analyse de l'asymétrie de la loi a posteriori des résidus du modèle. [source] The evolution of bipedal postures in varanoid lizardsBIOLOGICAL JOURNAL OF THE LINNEAN SOCIETY, Issue 3 2009GORDON W. SCHUETT The bipedal posture (BP) and gait of humans are unique evolutionary hallmarks, but similar stances and forms of locomotion have had enormous influences on a range of phylogenetically diverse tetrapods, particularly dinosaurs and birds, and a range of mammalian lineages, including non-human apes. The complex movements involved in bipedalism appear to have modest evolutionary origins, and it is presumed that a stable and erect posture is a prerequisite for erect strides and other bipedal movements. Facultative bipedalism in several lineages of lizards is achieved by running, but some varanid lizards (genus Varanus) exhibit BPs without running. In these cases, BPs (BPstanding) are not used as a form of locomotion; rather, BPstanding is associated with defensive displays, and such postures also probably permit better inspection of the environment. Yet, in other varanids, BPs have been observed only during combat episodes (BPcombat), where both contestants rise together and embrace in the so-called clinch phase. Numerous other species, however, show neither type of BP. Past researchers have commented that only large-bodied varanids exhibit BP, a behaviour that appears to show phylogenetic trends. We termed this idea the King,Green,Pianka (KGP) bipedal hypothesis. In this article, we address two main questions derived from the KGP hypothesis. First, what is the phylogenetic distribution of BP in Varanus and close relatives (varanoids)? Second, is BP positively correlated with the phylogenetic distribution of large body size (e.g. snout,vent length, SVL)? In addition, we asked a related question: do the lengths of the femur and tail show body size-independent adaptive trends in association with BP? Because varanid species that show BPstanding also use these postures during combat (BPcombat), both types of BP were analysed collectively and simply termed BP. Using comparative phylogenetic analyses, the reconstruction of BP required three steps, involving a single gain and two losses. Specifically, BP was widespread in the monophyletic Varanus, and the single gain occurred at the most recent common ancestor of the African clade. The two losses of BP occurred in different clades (Indo-Asian B clade and Indo-Australian Odatria clade). BPs are absent in the sister group to Varanus (Lanthanotus borneensis) and the other outgroup species (Heloderma spp.). Our phylogenetic reconstruction supports the KGP prediction that BP is restricted to large-bodied taxa. Using the Hansen model of adaptive evolution on a limited, but highly relevant morphological dataset (i.e. SVL; femur length, FL; tail length, TL), we demonstrated that these characters were not equivalent in their contribution to the evolution of BP in Varanus. SVL was significantly correlated with BP when modelled in a phylogenetic context, but the model identified random processes as dominant over adaptive evolution, suggesting that a body size threshold might be involved in the evolution of BP. A Brownian motion (BM) model outperformed the selection model in our analysis of relative TL, suggesting that TL and BP evolved independently. The selection model for relative FL outperformed the BM model, indicating that FL and BP share an adaptive history. Our non-phylogenetic analyses involving regression residuals of FL and TL vs. SVL showed no significant correlation between these characters and BP. We suggest that BP in Varanus provides a convergent or analogue model from which to investigate various forms of bipedalism in tetrapod vertebrates, especially other reptiles, such as theropod dinosaurs. Because BPstanding in varanids is possibly an incipient stage to some form of upright locomotion, its inclusion as a general model in evolutionary analyses of bipedalism of vertebrates will probably provide novel and important insights. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 97, 652,663. [source] | ||||||||||