scholarly journals Biological scaling analyses are more than statistical line fitting

2021 ◽  
Vol 224 (11) ◽  
Author(s):  
Douglas S. Glazier
Keyword(s):  
Body Size ◽  
Linear Regression ◽  
Traditional Method ◽  
Biological Traits ◽  
Log Transformation ◽  
Size Scaling ◽  
Non Linear ◽  
Scaling Analyses ◽  
Log Linear ◽  
Best Fit

ABSTRACT The magnitude of many biological traits relates strongly and regularly to body size. Consequently, a major goal of comparative biology is to understand and apply these ‘size-scaling’ relationships, traditionally quantified by using linear regression analyses based on log-transformed data. However, recently some investigators have questioned this traditional method, arguing that linear or non-linear regression based on untransformed arithmetic data may provide better statistical fits than log-linear analyses. Furthermore, they advocate the replacement of the traditional method by alternative specific methods on a case-by-case basis, based simply on best-fit criteria. Here, I argue that the use of logarithms in scaling analyses presents multiple valuable advantages, both statistical and conceptual. Most importantly, log-transformation allows biologically meaningful, properly scaled (scale-independent) comparisons of organisms of different size, whereas non-scaled (scale-dependent) analyses based on untransformed arithmetic data do not. Additionally, log-based analyses can readily reveal biologically and theoretically relevant discontinuities in scale invariance during developmental or evolutionary increases in body size that are not shown by linear or non-linear arithmetic analyses. In this way, log-transformation advances our understanding of biological scaling conceptually, not just statistically. I hope that my Commentary helps students, non-specialists and other interested readers to understand the general benefits of using log-transformed data in size-scaling analyses, and stimulates advocates of arithmetic analyses to show how they may improve our understanding of scaling conceptually, not just statistically.

Statistical Techniques for Interpreting Body Size–Related Exercise Performance during Growth

2000 ◽  
Vol 12 (2) ◽  
pp. 112-127 ◽  
Author(s):  
Joanne R. Welsman ◽  
Neil Armstrong
Keyword(s):  
Body Size ◽  
Linear Regression ◽  
Body Mass ◽  
Exercise Performance ◽  
Multilevel Regression ◽  
Cross Sectional ◽  
Regression Techniques ◽  
Ontogenetic Allometry ◽  
Log Linear ◽  
Individual Size

This paper reviews some of the statistical methods available for controlling for body size differences in the interpretation of developmental changes in exercise performance. For cross-sectional data analysis simple per body mass ratio scaling continues to be widely used, but is frequently ineffective as the computed ratio remains correlated with body mass. Linear regression techniques may distinguish group differences more appropriately but, as illustrated, only allometric (log-linear regression) scaling appropriately removes body size differences while accommodating the heteroscedasticity common in exercise performance data. The analysis and interpretation of longitudinal data within an allometric framework is complex. More established methods such as ontogenetic allometry allow insights into individual size-function relationships but are unable to describe adequately population effects or changes in the magnitude of the response. The recently developed multilevel regression modeling technique represents a flexible and sensitive solution to such problems allowing both individual and group responses to be modeled concurrently.

scholarly journals Age- and sex-dependent regression parameters for estimating live weight frim body measurements of West African Dwarf sheep

2021 ◽  
Vol 39 (1) ◽  
pp. 169-179
Author(s):  
O. S. Sowande ◽  
B. A Orebela ◽  
O. S Iyasere
Keyword(s):  
Body Size ◽  
Linear Regression ◽  
Regression Models ◽  
Live Weight ◽  
West African ◽  
The Body ◽  
Body Measurements ◽  
Age Group ◽  
Best Fit ◽  
Age And Sex

The relationships between live weight and eight body measurements of West African Dwarf (WAD) sheep were studied using 300 animals under farm condition. The animals were categorized based on age and sex. Data obtained on height at withers (HW), heart girth (HG), body length (BL), head length (HL), length of hindquarter (LHQ), width of hindquarter (WHQ), head width(HDW), and loin girth (LG) were fitted into simple linear (change in body measurement is directly proportional to weight or body size), allometric (body measurements do not necessarily change in direct proportion to weight or body size), and multiple linear regression models to predict live weight from the body measurements according to age group and sex. Results showed that live weight and body measurements of ewe were higher than that of the ram. Live weight, HG, HW, WHQ, LG, BL, LHQ, HL, and HW increased with the age of the animals. In multiple linear regression model, WHQ, LHQ, HW, HL and HDW best fit the model for sheep aged ≤1; HG, LG, BL and HDW for 2 year-old sheep; HG, BL, and HL best fit the model for sheep 3 years age group; LHQ best fit the model for sheep of 4 years of age; while HL best fits sheep that were in 5 year age category. Coefficients of determination (R2) values for linear and allometric models for predicting the live weight of WAD sheep increased with age in all the body measurements (HW, HG, BL, HL, LHQ, WHQ, HDW and LG). Sex had significant influence on the model with R2 values consistently higher in females except the models for LHQ, WHQ, LG and BL were they the same with the males. Based on R2 values, it was concluded that both linear and allometric regression models could be used to predict live weight from body measurements of WAD sheep.   

scholarly journals Correcting the Bias in the Practitioner Black-Scholes Method

2019 ◽  
Vol 12 (4) ◽  
pp. 157
Author(s):  
Yun Yin ◽  
Peter G. Moffatt
Keyword(s):  
Linear Regression ◽  
Implied Volatility ◽  
Option Price ◽  
Option Prices ◽  
Technical Problems ◽  
Black Scholes ◽  
Option Values ◽  
Non Linear ◽  
Alternative Means ◽  
Log Linear

We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the Black-Scholes formula to obtain predicted option prices. Firstly we ensure that the prediction from stage one is positive by using log-linear regression. Secondly, we correct the bias that results from the transformation applied to the fitted values (i.e., the Black-Scholes formula) being a highly non-linear function of implied volatility. We apply the smearing technique in order to correct this bias. An alternative means of implementing the PBS approach is to use the market option price as the dependent variable and estimate the parameters of the IV equation by the method of non-linear least squares (NLLS). A problem we identify with this method is one of model incoherency: the IV equation that is estimated does not correspond to the set of option prices used to estimate it. We use the Monte Carlo method to verify that (1) standard PBS gives biased option values, both in-sample and out-of-sample; (2) using standard (log-linear) PBS with smearing almost completely eliminates the bias; (3) NLLS gives biased option values, but the bias is less severe than with standard PBS. We are led to conclude that, of the range of possible approaches to implementing PBS, log-linear PBS with smearing is preferred on the basis that it is the only approach that results in valuations with negligible bias.

Removal of basic dyes from aqueous solutions by activated carbon derived from Eichornia crassipes: equilibrium and kinetic studies

2014 ◽  
Vol 49 (2) ◽  
pp. 163-178 ◽  
Author(s):  
Syed Usman Nasrin Banu ◽  
G. Maheswaran
Keyword(s):  
Activated Carbon ◽  
Linear Regression ◽  
Second Order ◽  
Isotherm Models ◽  
Batch Adsorption ◽  
Non Linear ◽  
Equilibrium Data ◽  
Pseudo Second Order ◽  
Eichornia Crassipes ◽  
Best Fit

The feasibility of preparing activated carbon from Eichornia crassipes by chemical activation was investigated. Batch experiments were carried out for the sorption of Methylene Blue (MB) and Rhodamine B (RB) onto the prepared activated carbon. The variables studied were initial dye concentration, pH, adsorbent dose, and contact time. Equilibrium data for the adsorption of the dyes onto activated carbon were obtained from batch adsorption experiments. Two-parameter isotherm models including Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich were employed for fitting equilibrium data. Three-parameter isotherm models including Redlich–Peterson, Toth, and Koble–Corrigan models were also employed for fitting the equilibrium data. Linear and non-linear regression methods were used to determine the best fit model to the equilibrium data. It was found that non-linear regression is a better method for determining isotherm parameters. The data were fitted to pseudo-first-order, pseudo-second-order, intraparticle diffusion model, and Elovich equation. The pseudo-second-order model gave the best fit to the equilibrium data as seen from correlation coefficient values. Fourier transform infrared spectroscopy and scanning electron microscopic investigations were carried out to confirm the morphological characteristics of the adsorbent. The prepared activated carbon had greater affinity for adsorbing MB when compared to RB.

Non-Linear Regression Forecast Model and Learning Algorithm Based on Functional Networks

2010 ◽  
Vol 159 ◽  
pp. 595-598
Author(s):  
Xiang Hu Liu
Keyword(s):  
Linear Regression ◽  
Linear Model ◽  
Traditional Method ◽  
Learning Algorithm ◽  
Forecast Model ◽  
Functional Networks ◽  
Non Linear ◽  
Linear Problems ◽  
Simulation Results ◽  
Forecast Function

Fitting of forecast function is very difficult and important in non-linear regression forecast problems. The accuracy is directly affected by the fitting of forecast function. Linear model replaced non-linear model in the traditional method is difficult to solve the problem when non-linear is stronger, and the result of fitting and forecast is not ideal. Functional network is a recently introduced extension of neural networks. It has certain advantages solving non-linear problems. Non-linear regression forecast model and learning algorithm based on functional networks is proposed in this article. Example about multi-variable non-linear regression forecast is provided. The simulation results demonstrate that forecast model based on Functional Networks whose accuracy of fitting and forecasting is more than some traditional methods have some value about theory and application.

Prediction of Surface Roughness and Optimization of Cutting Parameters in CNC Turning of Rotational Features

2020 ◽  
Vol 38 (8A) ◽  
pp. 1143-1153
Author(s):  
Yousif K. Shounia ◽  
Tahseen F. Abbas ◽  
Raed R. Shwaish
Keyword(s):  
Surface Roughness ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Feed Rate ◽  
Cutting Parameters ◽  
Spindle Speed ◽  
Depth Of Cut ◽  
Non Linear ◽  
Optimization Of Cutting Parameters

This research presents a model for prediction surface roughness in terms of process parameters in turning aluminum alloy 1200. The geometry to be machined has four rotational features: straight, taper, convex and concave, while a design of experiments was created through the Taguchi L25 orthogonal array experiments in minitab17 three factors with five Levels depth of cut (0.04, 0.06, 0.08, 0.10 and 0.12) mm, spindle speed (1200, 1400, 1600, 1800 and 2000) r.p.m and feed rate (60, 70, 80, 90 and 100) mm/min. A multiple non-linear regression model has been used which is a set of statistical extrapolation processes to estimate the relationships input variables and output which the surface roughness which prediction outside the range of the data. According to the non-linear regression model, the optimum surface roughness can be obtained at 1800 rpm of spindle speed, feed-rate of 80 mm/min and depth of cut 0.04 mm then the best surface roughness comes out to be 0.04 μm at tapper feature at depth of cut 0.01 mm and same spindle speed and feed rate pervious which gives the error of 3.23% at evolution equation.

Linear Regression Models for Interval-Valued Data using Log-transformation

2020 ◽  
Author(s):  
Nykolas Mayko Maia Barbosa ◽  
João Paulo Pordeus Gomes ◽  
César Lincoln Cavalcante Mattos ◽  
Diêgo Farias Oliveira
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Log Transformation ◽  
Interval Valued

scholarly journals Is There a Relationship between the Elasticity of Brain Tumors, Changes in Diffusion Tensor Imaging, and Histological Findings? A Pilot Study Using Intraoperative Ultrasound Elastography

2021 ◽  
Vol 11 (2) ◽  
pp. 271
Author(s):  
Santiago Cepeda ◽  
Sergio García-García ◽  
María Velasco-Casares ◽  
Gabriel Fernández-Pérez ◽  
Tomás Zamora ◽  
...  
Keyword(s):  
Brain Tumor ◽  
Diffusion Tensor Imaging ◽  
Linear Regression ◽  
Brain Tumors ◽  
Diffusion Tensor ◽  
Intraoperative Ultrasound ◽  
Ultrasound Elastography ◽  
Proliferation Index ◽  
Strong Positive Correlation ◽  
Non Linear

Intraoperative ultrasound elastography (IOUS-E) is a novel image modality applied in brain tumor assessment. However, the potential links between elastographic findings and other histological and neuroimaging features are unknown. This study aims to find associations between brain tumor elasticity, diffusion tensor imaging (DTI) metrics, and cell proliferation. A retrospective study was conducted to analyze consecutively admitted patients who underwent craniotomy for supratentorial brain tumors between March 2018 and February 2020. Patients evaluated by IOUS-E and preoperative DTI were included. A semi-quantitative analysis was performed to calculate the mean tissue elasticity (MTE). Diffusion coefficients and the tumor proliferation index by Ki-67 were registered. Relationships between the continuous variables were determined using the Spearman ρ test. A predictive model was developed based on non-linear regression using the MTE as the dependent variable. Forty patients were evaluated. The pathologic diagnoses were as follows: 21 high-grade gliomas (HGG); 9 low-grade gliomas (LGG); and 10 meningiomas. Cases with a proliferation index of less than 10% had significantly higher medians of MTE (110.34 vs. 79.99, p < 0.001) and fractional anisotropy (FA) (0.24 vs. 0.19, p = 0.020). We found a strong positive correlation between MTE and FA (rs (38) = 0.91, p < 0.001). A cubic spline non-linear regression model was obtained to predict tumoral MTE from FA (R2 = 0.78, p < 0.001). According to our results, tumor elasticity is associated with histopathological and DTI-derived metrics. These findings support the usefulness of IOUS-E as a complementary tool in brain tumor surgery.

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