The appropriate use of regression equations for the estimation of segmental inertia parameters

Linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct. In many cases theoretical relationships between such quantities are known and can be used as a basis for non-linear regression equations. This study compares linear and non-linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of Chandler et al. [Chandler et al. (1975) Investigation of inertial properties of the human body. AMRL Technical Report 74-137, Wright Patterson Air Force Base. OH.] Right limb data were used to derive the equations while left limb data were used as a cross-validation sample to evaluate the inertia estimates calculated from the equations. For the limb segments the standard error estimates had average values of 21% for the linear equations and 13% for the non-linear equations. Data on a 10 yr-old boy was used to compare the two approaches outside the sample range. The mean percentage residuals were 286% for the linear equations and 20% for the non-linear equations. A set of non-linear equations is provided.     

A new index of interactivity in parasite communities.

A new index of interactivity which allows objective evaluation and comparison of interactivity in communities between different host species is presented. The index is derived from the equations for species-accumulation curves generated using non-linear regression (with the Levenberg-Marquardt algorithm) of sample infracommunity richness data. It is advantageous in that it requires only presence/absence data to calculate, is applicable to all parasite taxa (including asexual species), is largely independent of sample size and allows objective comparison of parasite communities while correcting for differences in total richness. Iterative randomisation of infracommunity richness values to generate a mean value for the index avoids spurious results which may be generated by heterogeneity in infracommunity richness and the variation this produces in the non-linear regression results.     

Prediction of body composition in habitually active middle-aged men.

In 45 physically active men (ages 35-67 yr) who underwent hydrostatic weighing to determine body composition, multiple regression equations were developed for the prediction of body density (D), lean body weight (LBW), fat body weight (FBW), and % fat using selected anthropometric measurements. The prediction accuracy for these parameters using several previously generated anthropometric regression equations was also determined. With equations developed from the present data a substantially higher correlation was obtained between measured and predicted LBW (r = 0.95) than between measured and predicted D (r = 0.85), FBW (r = 0.88), or % fat (r = 0.84). When previously developed equations were applied to the present sample, correlations between measured and predicted values were considerably lower (4-42%) than in the original studies; this reduction was least in the case of LBW. Analysis of previous data indicated that in selected populations total body weight can account for a relatively large fraction of the variance in LBW. LBW may be estimated quite accurately (r greater than or equal to 0.90) in physically active men with one of several regression equations which include total body weight as an independent variable.     

Stature estimation in prehistoric Native Americans of Ohio

In the present report we investigate stature estimation techniques in a sample of 64 (35 male, 29 female) prehistoric Native Americans from Ohio. Because living stature is unknown for these 64 individuals, we use Fully's (1956) anatomical method to provide the best estimates of living stature. In this method all osseous components of skeletal height are measured and soft tissue correction is added. Comparisons of regression equations commonly used for stature estimation in prehistoric Eastern Woodland Native American populations, but developed for East Asian and East Asian-derived populations (using lower extremity components), show that these commonly used equations consistently yield stature estimates 2 to 8 cm in excess of the best estimates from Fully's method. Based on the skeletal height measures of the 64 individuals in the present sample, we develop regression equations for the estimation of stature. These equations yield stature estimates virtually identical to estimates from Fully's method and may prove useful for stature reconstruction in other prehistoric Eastern Woodland Native American populations.     

Estimation of skeletal muscle mass by bioelectrical impedance analysis.

The purpose of this study was to develop and cross-validate predictive equations for estimating skeletal muscle (SM) mass using bioelectrical impedance analysis (BIA). Whole body SM mass, determined by magnetic resonance imaging, was compared with BIA measurements in a multiethnic sample of 388 men and women, aged 18-86 yr, at two different laboratories. Within each laboratory, equations for predicting SM mass from BIA measurements were derived using the data of the Caucasian subjects. These equations were then applied to the Caucasian subjects from the other laboratory to cross-validate the BIA method. Because the equations cross-validated (i.e., were not different), the data from both laboratories were pooled to generate the final regression equation SM mass (kg) = [(Ht²/ R x 0.401) + (gender x 3.825) + (age x -0. 071)] + 5.102 where Ht is height in centimeters; R is BIA resistance in ohms; for gender, men = 1 and women = 0; and age is in years. The r(2) and SE of estimate of the regression equation were 0.86 and 2.7 kg (9%), respectively. The Caucasian-derived equation was applicable to Hispanics and African-Americans, but it underestimated SM mass in Asians. These results suggest that the BIA equation provides valid estimates of SM mass in healthy adults varying in age and adiposity.     

Prediction of body volume by a stepwise linear regression technique

Body volume and 35 anthropometric measurements were obtained from 88 active soldiers using standard techniques. These anthropometric measurements were examined for their possible relationships to body volume using stepwise linear regression analysis. Four measurements (Body weight, anterior thigh skinfold thickness, subscapular skinfold thickness and suprailiac skinfold thickness) accounted for 99.7% of the variation in body volume and the introduction of each of these measurements in the equation was significant. The regression equation for predicting body volume from these 4 anthropometric measurements had a multiple correlation coefficient of 0.9987 (P less than 0.001). Body weight alone was correlated with body volume to the extent of 0.9966. An attempt has therefore been made to develop a multiple linear regression equation without incorporation of body weight in the regression analysis. Nine measurements were selected by stepwise linear regression analysis for predicting body volume. These nine measurements accounted for 97.1% of the variation in body volume. These equations have been validated on another small sample of 22 soldiers. The analysis has also revealed that a direct regression of body density from the anthropometric variables gives more accurate results than when estimated body volumes are utilized for calculating body density.     

Weight of food and time required to satiate brown trout, Salmo trutta L.

Brown trout of different weights (range 8-358 g) were fed to satiation at fifteen different water temperatures (range 3.8–21.6°C. Both the weight of the trout (Wg) and the water temperature (T°C) affected the maximum weight of food (Q mg) consumed in a meal, and the relationship between the three variables was well described by a multiple regression equation which can be used to estimate the value of Q (with 95% confidence limits) for trout of different weights at different temperatures between 3.8°C and 21.6°C. The satiation time (with 95% confidence limits) can also be estimated from a multiple regression equation for trout of different weights at temperatures between 6.8°C and 18.1°C. Estimates from the multiple regression equations were applicable to a wide range of food organisms with the exception of larvae ofTenebrio molitor (mealworms). Appetite (measured by voluntary food intake) varied with temperature and was greatest between 13.3°C and 18.4°C. From comparisons with the results of other workers, it was concluded that the maximum amount of food consumed in a meal may provide sufficient calories for both the daily metabolic requirements and the daily maintenance requirements of a trout at temperatures between 3.8°C and 18.4°C, but not at temperatures above 18.4°C.     

灵芝子实体中三萜类物质抗肿瘤活性的谱效关系

通过HPLC指纹图谱结合多元线性回归分析对不同产地灵芝子实体的功效性特征进行评价,为寻找灵芝中活性三萜提供理论依据。利用高效液相分析方法,结合样品对肿瘤细胞L1210的增殖抑制率,运用“中药色谱指纹图谱相似度评价系统2004A版”软件和多元线性回归分析11批不同品种灵芝子实体中的三萜活性成分。样品与标准指纹图谱的相似度均在0.9以上,共标定了12个共有物质峰,其中与抗L1210肿瘤细胞活性关系密切的三萜物质有灵芝酸C₂、灵芝酸G、灵芝烯酸B、灵芝烯酸A、灵芝酸K、灵芝酸A、灵芝酸F和灵芝醛A。     

Specificity of training modalities on upper-body one repetition maximum performance: free weights vs. hammer strength equipment

The purpose of this study was to determine whether a relationship exists between 1-repetition maximum (1RM) performed on hammer strength (HS) machines compared to free weights (FWs) and also to develop regression equations that can accurately predict 1RM when switching from exercise modality to another. Thirty-one trained male subjects performed 1-RM lifts (1RM's) on 3 HS externally loaded machines and 3 comparable FW exercises. Subjects performed 2 1RM tests during each laboratory session, with at least 48-72 hours of recovery between each. One repetition maximum data were used to (a) determine the relationship between 1RM performed on HS vs. FW and (b) to develop regression equations that can accurately predict 1RM's when switching from 1 exercise modality to another. Statistics revealed significant differences (p < 0.05) between 1RM's performed on the HS equipment as compared to its corresponding (FW) exercise. For all exercises, 1RM's were significantly greater on the HS equipment. Regression equations were developed for all exercises, except when predicting the HS shoulder press and the HS preacher curls from their free weight counterparts, where no variables existed that could significantly predict their respective 1RM's. As 1 RMs were significantly greater when using the HS equipment compared to when using FWs, those transitioning from HS exercise to FW exercise should exercise caution.     

Body mass and stature estimation based on the first metatarsal in humans

Archaeological assemblages often lack the complete long bones needed to estimate stature and body mass. The most accurate estimates of body mass and stature are produced using femoral head diameter and femur length. Foot bones including the first metatarsal preserve relatively well in a range of archaeological contexts. In this article we present regression equations using the first metatarsal to estimate femoral head diameter, femoral length, and body mass in a diverse human sample. The skeletal sample comprised 87 individuals (Andamanese, Australasians, Africans, Native Americans, and British). Results show that all first metatarsal measurements correlate moderately to highly (r = 0.62-0.91) with femoral head diameter and length. The proximal articular dorsoplantar diameter is the best single measurement to predict both femoral dimensions. Percent standard errors of the estimate are below 5%. Equations using two metatarsal measurements show a small increase in accuracy. Direct estimations of body mass (calculated from measured femoral head diameter using previously published equations) have an error of just over 7%. No direct stature estimation equations were derived due to the varied linear body proportions represented in the sample. The equations were tested on a sample of 35 individuals from Christ Church Spitalfields. Percentage differences in estimated and measured femoral head diameter and length were less than 1%. This study demonstrates that it is feasible to use the first metatarsal in the estimation of body mass and stature. The equations presented here are particularly useful for assemblages where the long bones are either missing or fragmented, and enable estimation of these fundamental population parameters in poorly preserved assemblages.     

Regression equations for the estimation of stature and body mass using a Greek documented skeletal collection

Body size is an important variable in bioarchaeological and forensic studies, making the accurate calculation of stature and body mass imperative. Given that anatomical and morphometric approaches offer accurate results but require a particularly good preservation of the skeletal material, whereas mathematical and mechanical methods are more easily applicable but they are largely population-specific, the present paper uses a ‘hybrid’ approach in order to generate regression equations for the prediction of stature and body mass in a modern Greek sample. Specifically, anatomical and morphometric methods were used to calculate the stature and body mass of the individuals and regression equations using the Ordinary Least Squares and Reduced Major Axis methods were generated with long bone lengths and femoral head breadth as predictors. The obtained equations exhibit low random and directional error and perform better than existing equations designed using different samples from the United States, Europe, and the Balkans. Therefore, these equations are more appropriate for modern Greek material.     

Fecundity and egg density in the redd for sea trout

The relationship between fecundity and length for sea trout Salmo trutta from three streams in NW England was curvilinear and, after logarithmic transformation of both variables, was well described by a linear regression model. Regression equations for the fish from the three streams were not significantly different ( p >0.05). The relationship between estimated eggs per redd and female size in a tributary of one of the streams was also well described by a linear regression model after logarithmic transformation. Fecundity was usually higher than estimated eggs per redd, and this difference increased with female size so that the mean number of eggs per redd expressed as a percentage of mean fecundity decreased from 100% for a female with a length of 240 mm to 79% for one of 650 mm. The power function in its logarithmic form has now been fitted to fecundity-length data for sea trout from 12 streams and rivers in England, Scotland, Ireland and Norway. Comparisons between fecundity estimates for the same sizes of females revealed a large variation between populations and possible reasons for this are discussed.     

Conversion of logarithmic channel numbers into relative linear fluorescence intensity

We describe a simple, reproducible, and generally applicable method to assess the performance of log amplifiers by using a fluorescent sample that provides multiple peaks of different intensities. The channel differences between multiple peaks are used to evaluate the logarithmic behavior of the fluorescence signal amplifier on the flow cytometer. A calibration curve can be created to correct the channel numbers for deviations from true logarithmic behavior and then convert data into relative linear intensities. By using these linear fluorescent intensities, we compared the capacity of different antisera against HIV-1 (human immunodeficiency virus type 1) peptides to inhibit the binding of HIV-1 to CEM, a CD4-positive T-cell line. A wide range of applications for this calibration procedure can be envisioned and the method is valuable for monitoring instrument performance over time.     

Rapid estimation of nutrients in chicken manure during plant-field composting using physicochemical properties

Regression equations which relate livestock and poultry manure nutrient content to its several physicochemical properties have been reported by previous researchers. This study explores the feasibility and efficiency to determine the nutrients (TN; TP; TK; Cu and Zn) in chicken manure during composting using physicochemical properties (pH, EC and DM), and compares the performances of regression equations in this study with those in the literature. The results show that DM is the best predictor to construct the single linear regressions for all the nutrients (R2≥0.84, p<0.001). In addition, the multiple linear regression equations based on DM and pH are all notable. These findings show the potential of physicochemical models for TN, TP, TK, Cu and Zn with more convenience and rapidness, but further research is needed to develop better models with higher accuracy for the above and other more nutrients.     

Flow cytometric enumeration of absolute lymphocyte number in peripheral blood using two parameters of light scatter

A method was developed to measure the absolute lymphocyte count (ALC) of whole blood using the Spectrum III automated flow cytometer. Ninety-nine samples of human peripheral blood were analysed on the Spectrum and the Coulter Counter S Plus II, to allow for comparison of the two machines. Regression analysis was used to test the extent of agreement between the sets of measurements on the two machines. The results demonstrated that the slope of the regression line was not significantly different from one, indicating a high level of correlation between Spectrum and Coulter ALC's. However, the mean difference between Coulter and Spectrum ALC's was not equal to zero, with the Spectrum giving counts approximately 10% lower than those of the Coulter machine. This is attributed to the different ways by which the two machines define a lymphocyte, the Spectrum III by two parameters of light scatter and the Coulter S Plus II by the single parameter of cell volume.     

One-step analysis of seed storage data and the longevity of Arabidopsis thaliana seeds

Seeds of two ecotypes of Arabidopsis thaliana, NW20 and N1601, were aged over a range of saturated salt solutions at temperatures between 6 degrees C and 55 degrees C. For each ecotype, the results from 37 storage experiments were summarized using the Ellis and Roberts viability equations and a modified version of these equations which allows for a proportion of 'non-respondents'. For both models, two approaches were taken in order to model the effect of moisture content (MC) and temperature on seed longevity. The first, a two-step approach, involved fitting individual survival curves and then multiple regression analysis of the fitted parameters on moisture content and temperature. For the second approach, the full viability models were fitted in one step, including the multiple regression for the effects of MC and temperature within the generalized linear model used to describe each survival curve. This one-step approach takes into account the full variability of the data and provides the best predictions of seed longevity based on the original assumptions of the Ellis and Roberts viability equations. As a consequence of taking into account all the variation, this one-step approach is more sensitive and thus more likely to detect changes due to reducing the number of parameters in the model as being significant. Whilst both approaches indicated that seeds from the two Arabidopsis ecotypes have the same response to MC and temperature, parameter values did differ between the approaches, with the one-step approach providing the better fit. The best model for these two ecotypes, from the one-step approach, confirmed a quadratic relationship between temperature and longevity, but the magnitude of the non-linearity is not as large as indicated by the universal value for the quadratic term.     

Comparing Machine Learning Classifiers and Linear/Logistic Regression to Explore the Relationship between Hand Dimensions and Demographic Characteristics

Understanding the relationship between physiological measurements from human subjects and their demographic data is important within both the biometric and forensic domains. In this paper we explore the relationship between measurements of the human hand and a range of demographic features. We assess the ability of linear regression and machine learning classifiers to predict demographics from hand features, thereby providing evidence on both the strength of relationship and the key features underpinning this relationship. Our results show that we are able to predict sex, height, weight and foot size accurately within various data-range bin sizes, with machine learning classification algorithms out-performing linear regression in most situations. In addition, we identify the features used to provide these relationships applicable across multiple applications.     

Evaluation of Sampling-Based Methods for Sensitivity Analysis: Case Study for the E. coli Food Safety Process Risk Model

This article evaluates selected sensitivity analysis methods applicable to risk assessment models with two-dimensional probabilistic frameworks, using a microbial food safety process risk model as a test-bed. Six sampling-based sensitivity analysis methods were evaluated including Pearson and Spearman correlation, sample and rank linear regression, and sample and rank stepwise regression. In a two-dimensional risk model, the identification of key controllable inputs that can be priorities for risk management can be confounded by uncertainty. However, despite uncertainty, results show that key inputs can be distinguished from those that are unimportant, and inputs can be grouped into categories of similar levels of importance. All selected methods are capable of identifying unimportant inputs, which is helpful in that efforts to collect data to improve the assessment or to focus risk management strategies can be prioritized elsewhere. Rank-based methods provided more robust insights with respect to the key sources of variability in that they produced narrower ranges of uncertainty for sensitivity results and more clear distinctions when comparing the importance of inputs or groups of inputs. Regression-based methods have advantages over correlation approaches because they can be configured to provide insight regarding interactions and nonlinearities in the model.