Estimating the body mass of extinct ungulates: a study on the use of multiple regression

Body size is correlated with virtually every morphological, physiological, and life-history trait in mammal species. As a consequence, estimates of body size of fossil species are often used for paleoecological reconstructions. Characters used as proxies for body mass in extinct species include teeth, skull, and skeletal measurements. We show that the body-mass estimates of extinct species from living taxa can be misleading and depend largely on the morphological variable selected as a proxy for body mass. We also discuss statistical tools that are available to assess the accuracy of body-mass estimates in extinct species. Here, we focus on the revision of the mass estimate of the giant Miocene fossil rodent Phoberomys pattersoni (Venezuela), the 2nd largest rodent ever reported, with an estimated body mass between 436 and 741 kg. This is far beyond the range of average body masses in living rodents, which vary from several grams to 40 kg. We conclude that body mass of Phoberomys was most likely overestimated. The species P. pattersoni likely weighed between 220 kg and 280 kg, the mass of a horse or a large antelope.

An attempt has been made to evolve some simple multiple linear regression equations for the prediction of VO2 max from body weight, time for 3.2 km run and exercise dyspnoeic index ( DIstd Ex%). The predictor variables have been selected by examining the product moment correlations of body weight, relative body weight indices, time for 3.2 km run, chest expansion, height, and DIstd Ex% with VO2 max, based on data collected on 320 healthy Indian males (17-22 years). It has been observed that body weight, time for 3.2 km run and DIstd Ex% attained maximum correlations with VO2 max. Thus, two regression equations with two and three predictor variables have been established in this paper to predict VO2 max. The first regression equation yielded a multiple correlation of 0.608 (P less than 0.001) with a standard error of 0.214 1 X min-1. In this equation, body weight and time for 3.2 km run were considered as significant predictors. To increase the precision of this equation, another multiple linear regression equation based on body weight, time for 3.2 km run and DIstd Ex% as predictors has been developed. This equation yielded a multiple correlation of 0.658 (P less than 0.001) with a standard error of 0.204 1 X min-1. Applications of these regression equations will be of practical importance to biomedical scientists engaged in the development of a simple procedure for indirect assessment of VO2 max, and may serve well as preliminary screening procedures for personnel selection.

Chapter 5 addresses advanced applications of the basic multiple regression model. Most of this chapter is devoted to the use of multiple regression in performing the analysis of variance (ANOVA). Be prepared; I will introduce the topic from a very different approach than you have probably been taught. The way it is taught here and in many other multivariate texts uses multiple regression, not the approach generally called “partitioning of sums of squares.” The results are identical to the way it is taught in basic statistics and experimental design courses, but use of multiple regression greatly simplifies many computations, especially those arising when the number of subjects in the various groups differs (the unequal-N case). One reason the ANOVA is not taught as a special case of multiple regression in undergraduate statistics courses is that it would be too difficult to cover basic material on multiple regression like that in Chapter 4 first. Teaching the ANOVA as a special case of multiple regression has the advantage of illustrating the way computer packages operate, since the packages do not use the methods you were taught as an undergraduate.

BackgroundEach year numerous studies evaluate longitudinal data within a lifecourse context with later-life health status (e.g. blood pressure) analysed with respect to repeated measures of early-life experiences (e.g. body mass)...

The Rothamsted Insect Survey has kept records of aerial aphid activity using suction traps since 1965. Previous work has shown that, for certain species, there is a linear relationship between the date of first record in the trap each year and the mean temperature during the preceding winter. This paper describes and evaluates a more complex technique which relates the date of first record to a range of weather variables over 28 winter time periods. The technique uses principle components analysis to remove correlations between weather variables before these are regressed on the date of first record. Data from 1966 to 1988 inclusive are used to generate models to predict the date of first record of Myzus persicae (Sulzer) at Rothamsted, and the predictive values of models using both simple and multiple regression are assessed using data from 1989 to 1992. The accuracy of the multiple regression models was no greater than that of the simple regression models during these years. However, the multiple regression approach identified relationships with other variables for time periods when the correlation with mean temperature was weaker and may therefore be more widely applicable.

The recent debate about the taxation assessments of Domesday Book has raised questions both of statistical technique and of historical interpretation.2 McDonald and Snooks stress the superiority of their methodological approach in this context over simple linear regression. They believe that their use of multiple regression has clearly revealed evidence that hidation was a sophisticated process of taxation assessment based on a mix of manorial resources. Hamshere points out the difficulties of reconciling the implications of this hypothesis with the historical context from which the data have come. One point which touches consideration of both technique and interpretation concerns the frequency with which multiples of five are found among the hidages in Domesday Book. The significance attached to the five-hide tendency by Round is at the heart of the 'conventional wisdom' which McDonald and Snooks seek to demolish in the interpretation of their own studies.3 It is the basis of Round's assertion that hidages were allocated downwards through an administrative hierarchy.4 Hamshere's analysis of seven counties yields evidence of this tendency which is more compatible with Round's ideas than those of McDonald and Snooks, but he speaks only of Domesday entries, because he shares their suspicion of Round's extension of the argument to vills which he has himself 'reconstituted' by combining entries. The point is, however, worthy of further consideration. Belief in the validity of the conclusions drawn from the multiple regressions under debate effectively depends upon the assumption that Round was completely wrong to see individual hidages as subdivisions of rounded assessments for vills, since it carries with it the implication that these hidages were assessed independently of each other. McDonald and Snooks do not address the question directly in their analyses, but they suggest that five-hide multiples result from a natural tendency towards rounding by the Domesday assessors. A recent study of Buckinghamshire's Domesday hidages reinforces the findings in Hamshere's seven counties and yields further evidence to suggest

6 - Issues in the Use and Application of Multiple Regression Analysis

Multiple regression is one of the most used statistical methods in social science research. If we examine the existing literature in business, we would find out that multiple regression is indeed heavily adopted as the research tool to account for the social phenomena and test the designated hypotheses. However, if we look into the selected studies in the literature more closely, we would amazingly understand that the use of multiple regression is not always appropriate and the findings or implications derived from the method are therefore doubtful. The purpose of this study is to address this major problem in the business literature and suggest critically the proper use of the important research tool of multiple regression.

The effect of the variation of lipid droplet volume on individual carbon content was studied in two species of planktonic freshwater copepods, Eudiaptomus gracilis G.O. Sars and Thermocyclops oithonoides G.O. Sars. It was found, that when a multiple regression of carbon content on prosoma and lipid droplet volume instead of a simple regression of carbon content on prosoma volume was applied, the unexplainied variance of individual carbon content of Eudiaptomus gracilis could be reduced. However, the use of multiple regression on Thermocyclops oithonoides data did not lead to significantly higher coefficient of determination than was obtained by using a simple regression.

Estimating the body mass of Pleistocene canids: discussion of some methodological problems and a new ‘taxon free’ approach

Vitamin B-12, folate, iron, and vitamin A concentrations in rural Indian children are associated with continued breastfeeding, complementary diet, and maternal nutrition

This study aims to determine and test empirical data related to interpersonal communication and teacher social competence on eacher social behavior separately or simultaneously In this study the authors used a survey method, with correlational techniques and simple and multiple regression analysis Samples were taken from a population of.83 from a total of 104 student populations at Madrasah Aliyah Darul Marhamah. Data collection techniques using questionnaires, observation, and documentary studies. The data analysis technique used descriptive analysis model, correlation coefficient, simple regression analysis and multiple regression. The type of analysis used is correlation analysis and simple regression and multiple regression which are described descriptively. The results of this study indicate that: First, there is a positive effect of interpersonal communication on students' social behavior based on the results of the partial T test.in.multiple linear.regression analysis, with a large effect of 12.3%, and the simple linear regression equation shows Ŷ = 52.151 + 0.644 X1 which means that every one unit score increase Interpersonal communication, will have an influence on increasing the score of social behavior by 52,794. Second, there is a positive influence on the social competence of teachers on students' social behavior based on the results of the partial T test in multiple linear regression analysis, with a magnitude of influence of 12%, and the simple linear regression equation shows Ŷ = 93.895 + 0.289X2 which means that every one unit increase in the social competency score will have an effect on the increase in students' social behavior scores by 94,184. Third, there is an effect of interpersonal communication and teacher social competence on student social behavior based on the results of the simultaneous F test (F test) in multiple linear regression analysis, with a large effect of 19.8%, and the multiple linear regression equation shows Ŷ = 74.673 + 0.263X1 + 0.234X2. This means that any increase in the score of interpersonal communication and social competence of teachers together or simultaneously, will have an effect on improving student social behavior, amounting to 75.170

ABSTRACTAim The aim of this study is to determine the patterns of nitrogen (N) concentrations in leaf litter of forest trees as functions of climatic factors, annual average temperature (Temp, °C) and annual precipitation (Precip, dm) and of forest type (coniferous vs. broadleaf, deciduous vs. evergreen, Pinus, etc.).Location The review was conducted using data from studies across the Eurasian continent.Methods Leaf litter N concentration was compiled from 204 sets of published data (81 sets from coniferous and 123 from broadleaf forests in Eurasia). We explored the relationships between leaf litter N concentration and Temp and Precip by means of regression analysis. Leaf litter data from N2‐fixing species were excluded from the analysis.Results Over the Eurasian continent, leaf litter N concentration increased with increasing Temp and Precip within functional groups such as conifers, broadleaf, deciduous, evergreen and the genus Pinus. There were highly significant linear relationships between ln(N) and Temp and Precip (P < 0.001) for all available data combined, as well as for coniferous trees, broadleaf trees, deciduous trees, evergreen trees and Pinus separately. With both Temp and Precip as independent variables in multiple regression equations, the adjusted coefficient of determination () was evidently higher than in simple regressions with either Temp or Precip as independent variable. Standardized regression coefficients showed that Temp had a larger impact than Precip on litter N concentration for all groups except evergreens. The impact of temperature was particularly strong for Pinus.Conclusions The relationship between leaf litter N concentration and temperature and precipitation can be well described with simple or multiple linear regression equations for forests over Eurasia. In the context of global warming, these regression equations are useful for a better understanding and modelling of the effects of geographical and climatic factors on leaf litter N at a regional and continental scale.

Multiple meaningful ecological characterizations of a species revolve around body mass. Because body mass cannot be directly measured in extinct taxa, reliable body mass predictors are needed. Many published body mass prediction equations rely on dental dimensions, but certain skeletal dimensions may have a more direct and consistent relationship with body mass. We seek to evaluate the reliability of prediction equations for inferring euarchontan body mass based on measurements of the articular facet areas of the astragalus and calcaneus. Surface areas of five astragalar facets (n = 217 specimens) and two calcaneal facets (n = 163) were measured. Separate ordinary least squares and multiple regression equations are presented for different levels of taxonomic inclusivity, and the reliability of each equation is evaluated with the coefficient of determination, standard error of the estimate, mean prediction error, and the prediction sum of squares statistic. We compare prediction errors to published prediction equations that utilize dental and/or tarsal measures. Finally, we examine the effects of taxonomically specific regressions and apply our equations to a diverse set of non-primates. Our results reveal that predictions based on facet areas are more reliable than most linear dental or tarsal predictors. Multivariate approaches are often better than univariate methods, but require more information (making them less useful for fragmentary fossils). While some taxonomically specific regressions improve predictive ability, this is not true for all primate groups. Among individual facets, the ectal and fibular facets of the astragalus and the calcaneal cuboid facet are the best body mass predictors. Since these facets have primarily concave curvature and scale with positive allometry relative to body mass, it appears that candidate skeletal proxies for body mass can be identified based on their curvature and scaling coefficients.

This study measured the relative contributions of age, gender, body weight, and resting heart rate to lift capacity in 531 healthy employed males and females in a cross-sectional model. The objectives of this study were to measure the contributions to lift capacity that are made by these variables and to develop an appropriate means to express the results of a new test of lift capacity. A formal training program was developed and administered to 110 health care professionals. Subsequently, each trained evaluator performed five tests on healthy volunteers. The effect of the independent variables were studied through the use of multiple regression and analysis of variance procedures. Results indicate that age, resting heart rate, and body weight are significant predictors of performance, with the last variable being the most important. A method to normalize lift capacity is presented in which the maximum acceptable weight lifted is divided by the evaluee's body weight to derive relative acceptable weight, a variable which is normally distributed. Those who use measures of lift capacity to describe performance must consider the effect of these variables in order to make valid interpretations of lift capacity test performance.