scholarly journals Technical Note: Nominal Stiffness Evaluation and Regression Analysis of GT-2 Rubber-Fiberglass Timing Belts

2018 ◽  
Author(s):  
Bozun Wang ◽  
Yefei Si ◽  
Charul Chadha ◽  
James T. Allison ◽  
Albert E. Patterson
Keyword(s):  
Regression Analysis ◽  
Regression Models ◽  
Linear Models ◽  
System Modeling ◽  
Technical Note ◽  
Effective Stiffness ◽  
Modeling Error ◽  
Mechatronic Systems ◽  
Stiffness Evaluation ◽  
Best Fit

GT-style rubber-fiberglass (RF) timing belts are designed to effectively transfer rotational motion from pulleys to linear motion in small machines and mechatronic systems. One of the characteristics of belts under this type of loading condition is that the length between load and pulleys changes during operation, thereby changing their effective stiffness. It has been shown that the effective stiffness of such a belt is a function of a "nominal stiffness" and the real-time belt section lengths. However, this nominal stiffness is not necessarily constant; it is common to assume linear proportional stiffness, but this often results in system modeling error. This technical note describes a brief study where the nominal stiffness of two lengths (400 mm and 760 mm ) of GT-2 RF timing belts was tested up to breaking point; regression analysis was performed on the results to best model the observed stiffness. The study was replicated three times, providing a total of six stiffness curves. It was found that cubic regression models (R^2 > 0.999) were the best fit, but that quadratic and linear models still provided acceptable representations of the whole dataset with R^2 values above 0.940.

scholarly journals Nominal Stiffness of GT-2 Rubber-Fiberglass Timing Belts for Dynamic System Modeling and Design

Robotics ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 75
Author(s):  
Bozun Wang ◽  
Yefei Si ◽  
Charul Chadha ◽  
James Allison ◽  
Albert Patterson
Keyword(s):  
Loading Condition ◽  
Linear Models ◽  
System Modeling ◽  
Technical Note ◽  
Effective Stiffness ◽  
Modeling Error ◽  
Mechatronic Systems ◽  
Timing Belt ◽  
Dynamic System Modeling ◽  
Best Fit

GT-style rubber-fiberglass (RF) timing belts are designed to effectively transfer rotational motion from pulleys to linear motion in robots, small machines, and other important mechatronic systems. One of the characteristics of belts under this type of loading condition is that the length between load and pulleys changes during operation, thereby changing their effective stiffness. It has been shown that the effective stiffness of such a belt is a function of a “nominal stiffness” and the real-time belt section lengths. However, this nominal stiffness is not necessarily constant; it is common to assume linear proportional stiffness, but this often results in system modeling error. This technical note describes a brief study where the nominal stiffness of two lengths ( 400 m m and 760 m m ) of GT-2 RF timing belt was tested up to breaking point; regression analysis was performed on the results to best model the observed stiffness. The experiments were performed three times, providing a total of six stiffness curves. It was found that cubic regression mod els ( R 2 > 0.999 ) were the best fit, but that quadratic and linear models still provided acceptable representations of the whole dataset with R 2 values above 0.940 .

scholarly journals Model-based Informal Inference

2017 ◽  
Vol 6 (5) ◽  
pp. 140
Author(s):  
Theodosia Prodromou
Keyword(s):  
Linear Regression ◽  
Instructional Practices ◽  
Linear Model ◽  
Regression Models ◽  
Linear Models ◽  
Linear Regression Models ◽  
Journal Paper ◽  
Support Students ◽  
Best Fit ◽  
Informal Inference

Following recent scholarly interest in teaching informal linear regression models, this study looks at teachers’ reasoning about informal lines of best fit and their role in pedagogy. The case results presented in this journal paper provide insights into the reasoning used when developing a simple informal linear model to best fit the available data. This study also suggests potential in specific aspects of bidirectional modelling to help foster the development of robust knowledge of the logic of inference for those investigating and coordinating relations between models developed during modelling exercises and informal inferences based on these models. These insights can inform refinement of instructional practices using simple linear models to support students’ learning of statistical inference, both formal and informal.

scholarly journals Unweighted regression models perform better than weighted regression techniques for respondent-driven sampling data: results from a simulation study

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Lisa Avery ◽  
Nooshin Rotondi ◽  
Constance McKnight ◽  
Michelle Firestone ◽  
Janet Smylie ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Regression Models ◽  
Linear Models ◽  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Respondent Driven Sampling ◽  
Regression Techniques ◽  
Coverage Rates ◽  
Low Prevalence

Abstract Background It is unclear whether weighted or unweighted regression is preferred in the analysis of data derived from respondent driven sampling. Our objective was to evaluate the validity of various regression models, with and without weights and with various controls for clustering in the estimation of the risk of group membership from data collected using respondent-driven sampling (RDS). Methods Twelve networked populations, with varying levels of homophily and prevalence, based on a known distribution of a continuous predictor were simulated using 1000 RDS samples from each population. Weighted and unweighted binomial and Poisson general linear models, with and without various clustering controls and standard error adjustments were modelled for each sample and evaluated with respect to validity, bias and coverage rate. Population prevalence was also estimated. Results In the regression analysis, the unweighted log-link (Poisson) models maintained the nominal type-I error rate across all populations. Bias was substantial and type-I error rates unacceptably high for weighted binomial regression. Coverage rates for the estimation of prevalence were highest using RDS-weighted logistic regression, except at low prevalence (10%) where unweighted models are recommended. Conclusions Caution is warranted when undertaking regression analysis of RDS data. Even when reported degree is accurate, low reported degree can unduly influence regression estimates. Unweighted Poisson regression is therefore recommended.

scholarly journals Retention of the Antibiotic Cefuroxime onto Agricultural and Forest Soils

2021 ◽  
Vol 11 (10) ◽  
pp. 4663
Author(s):  
Raquel Cela-Dablanca ◽  
Carolina Nebot ◽  
Lucia Rodríguez López ◽  
David Ferández-Calviño ◽  
Manuel Arias-Estévez ◽  
...  
Keyword(s):  
Forest Soils ◽  
Linear Models ◽  
Agricultural Soils ◽  
Organic Matter Content ◽  
Matter Content ◽  
Batch Type ◽  
Exchangeable Ca ◽  
Influence Of Ph ◽  
Best Fit ◽  
Soil Colloids

Antibiotics in wastewater, sewage sludge, manures, and slurries constitute a risk for the environment when spread on soils. This work studies the adsorption and desorption of the antibiotic cefuroxime (CFX) in 23 agricultural and forest soils, using batch-type experiments. Our results show that the adsorption values were between 40.75 and 99.57% in the agricultural soils, while the range was lower (from 74.57 to 93.46%) in forest soils. Among the Freundlich, Langmuir, and Linear models, the Freundlich equation shows the best fit for the adsorption results. In addition, agricultural soils with higher pH are the ones that present the highest adsorption. Further confirmation of the influence of pH on adsorption is given by the fact that Freundlich’s KF parameter and the Linear model Kd parameter shows a positive correlation with pH and with the exchangeable Ca and Mg values, which are known to affect the charges of the soil colloids and the formation of cationic bridges between adsorbents and adsorbate. In addition, Freundlich’s n parameter shows a positive and significant correlation with the organic matter content, related to the high adsorption taking place on forest soils despite their pH < 5. Regarding desorption, in most cases, it is lower than 1%, which indicates that CFX is adsorbed in a rather irreversible way onto these soils. Overall, these results can be considered relevant regarding their potential impact on environmental quality and public health.

scholarly journals Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 609
Author(s):  
María del Mar Rueda ◽  
Beatriz Cobo ◽  
Antonio Arcos
Keyword(s):  
Regression Analysis ◽  
Regression Models ◽  
Regression Coefficients ◽  
Randomized Response ◽  
Statistical Tool ◽  
Complex Survey ◽  
Complex Sample ◽  
Qualitative Variables ◽  
World Survey ◽  
Sensitive Variable

Randomized response (RR) techniques are widely used in research involving sensitive variables, such as drugs, violence or crime, especially when a population mean or prevalence must be estimated. However, they are not generally applied to examine relationships between a sensitive variable and other characteristics. This type of technique was initially applied to qualitative variables, and studies later showed that a logistic regression may be performed with RR data. Since many of the variables considered in this context are quantitative, RR techniques were extended to these cases to estimate the values required. Regression analysis is a valuable statistical tool for exploring relationships among variables and for establishing associations between responses and covariates. In this article, we propose a design-based regression analysis for complex sample designs based on the unified RR approach. We present estimators of the regression coefficients, study their theoretical properties and consider different ways to estimate their variance. The properties of these estimation techniques were simulated using various quantitative randomized models. The method proposed was also used to analyse the findings from a real-world survey.

Risperidone-treated Children and Adolescents with Behavioral Disorders: Do Drug Dose and Patients’ Gender and Age Relate to Drug and Metabolite Plasma Levels?

2017 ◽  
Vol 41 (S1) ◽  
pp. S104-S104
Author(s):  
D. Piacentino ◽  
M. Grözinger ◽  
A. Saria ◽  
F. Scolati ◽  
D. Arcangeli ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Children And Adolescents ◽  
Behavioral Disorders ◽  
Plasma Levels ◽  
Linear Models ◽  
Parent Drug ◽  
Drug Dose ◽  
Cut Elimination ◽  
Younger Patients ◽  
Gender And Age

IntroductionBehavioral disorders, such as conduct disorder, influence choice of treatment and its outcome. Less is known about other variables that may have an influence.Objectives/AimsWe aimed to measure the parent drug and metabolite plasma levels in risperidone-treated children and adolescents with behavioral disorders and investigate the role of drug dose and patients’ gender and age.MethodsWe recruited 115 children/adolescents with DSM-5 behavioral disorders (females = 24; age range: 5–18 years) at the Departments of Psychiatry of the Hospitals of Bolzano, Italy, and Innsbruck, Austria. We measured risperidone and its metabolite 9-hydroxyrisperidone plasma levels and the parent drug-to-metabolite ratio in the plasma of all patients by using LC-MS/MS. A subsample of 15 patients had their risperidone doses measured daily. We compared risperidone and 9-hydroxyrisperidone plasma levels, as well as risperidone/9-hydroxyrisperidone ratio, in males vs. females and in younger (≤ 14 years) vs. older (15–18 years) patients by using Mann-Whitney U test. We fitted linear models for the variables “age” and “daily risperidone dose” by using log-transformation, regression analysis and applying the R2 statistic.ResultsFemales had significantly higher median 9-hydroxyrisperidone plasma levels (P = 0.000). Younger patients had a slightly lower median risperidone/9-hydroxyrisperidone ratio (P = 0.052). At the regression analysis, daily risperidone doses and metabolite, rather than parent drug–plasma levels were correlated (R2 = 0.35).ConclusionsGender is significantly associated with plasma levels, with females being slower metabolizers than males. Concerning age, younger patients seem to be rapid metabolizers, possibly due to a higher activity of CYP2D6. R2 suggests a clear-cut elimination of the metabolite.Disclosure of interestThe authors have not supplied their declaration of competing interest.

scholarly journals Estimation of Outdoor PM2.5 Infiltration into Multifamily Homes Depending on Building Characteristics Using Regression Models

2021 ◽  
Vol 13 (10) ◽  
pp. 5708
Author(s):  
Bo-Ram Park ◽  
Ye-Seul Eom ◽  
Dong-Hee Choi ◽  
Dong-Hwa Kang
Keyword(s):  
Regression Analysis ◽  
Correlation Analysis ◽  
Field Test ◽  
Outer Surface ◽  
Regression Models ◽  
Field Tests ◽  
Test Results ◽  
Correlation And Regression Analysis ◽  
Building Characteristics ◽  
Pm2.5 Concentration

The purpose of this study was to evaluate outdoor PM2.5 infiltration into multifamily homes according to the building characteristics using regression models. Field test results from 23 multifamily homes were analyzed to investigate the infiltration factor and building characteristics including floor area, volume, outer surface area, building age, and airtightness. Correlation and regression analysis were then conducted to identify the building factor that is most strongly associated with the infiltration of outdoor PM2.5. The field tests revealed that the average PM2.5 infiltration factor was 0.71 (±0.19). The correlation analysis of the building characteristics and PM2.5 infiltration factor revealed that building airtightness metrics (ACH50, ELA/FA, and NL) had a statistically significant (p < 0.05) positive correlation (r = 0.70, 0.69, and 0.68, respectively) with the infiltration factor. Following the correlation analysis, a regression model for predicting PM2.5 infiltration based on the ACH50 airtightness index was proposed. The study confirmed that the outdoor-origin PM2.5 concentration in highly leaky units could be up to 1.59 times higher than that in airtight units.

Regression analysis of longitudinal covariates with censored and longitudinal outcome

2018 ◽  
Author(s):  
◽  
Li Chen
Keyword(s):  
Regression Analysis ◽  
Longitudinal Data ◽  
Linear Models ◽  
Partial Likelihood ◽  
Response Variable ◽  
Additive Hazards ◽  
Time Points ◽  
Longitudinal Outcome ◽  
Longitudinal Covariates ◽  
Weighting Technique

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Longitudinal data contain repeated measurements of variables on the same experimental subject. It is often of interest to analyze the relationship between these variables. Typically, there is one or several longitudinal covariates and a response variable that can be either longitudinal or time to an event. Regression models can be employed to analyze these relationships. Ideally, longitudinal variables should be continuously monitored and their complete trajectories along the time are observed. Practically, however, this is unrealistic, either economically or methodologically. Often one only obtains so called sparse longitudinal data, where variables are intermittently observed at relatively sparse time points within the period of study. Such sparse longitudinal data give rise to an issue for the analysis of the response of time to an event, where survival analysis is typically implemented, e.g. the Cox model or additive hazards model. In both models, the values of covariates of all subjects at risk are needed in order to calculate the partial likelihood. But in the case of sparse longitudinal data, the availability of these observations may not be satis fied. Moreover, if the response variable is also longitudinal, it is possible that the response and covariates are not observed altogether, or at least not close to each other enough to be considered as observed simultaneously. Although a wealth of studies have been dedicated to longitudinal data analysis, very few of them have seriously considered and rigorously studied the situation aforementioned. In this dissertation, we discuss the regression analysis of longitudinal cavities with censored and longitudinal outcome. To be specific, Chapter 2 targets the additive hazards models with sparse longitudinal covariates, Chapter 3 studies the partially linear models with longitudinal covariates and response observed at mismatched time points, also known as asynchronous longitudinal data, and Chapter 4 explores longitudinal data with more complex structures with linear models. Kernel weighting technique is the key idea to all the stated researches. Estimators are derived based on kernel weighting technique and their asymptotical properties were rigorously examined, along with simulation studies for their fi nite sample performance, and illustrations using real data sets.

scholarly journals Are We Drawing the Correct Conclusions? Regression Analysis in the Nonprofit Literature

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
Robert Shearer ◽  
Truman Clark
Keyword(s):  
Regression Analysis ◽  
Linear Models ◽  
Type Ii ◽  
Type Ii Errors ◽  
Analytical Tools

Linear models are the most commonly used analytical tools in the nonprofit literature. Academics and practitioners utilize these models to test different hypotheses in support of their research efforts, seeking to find significant results that substantiate their theories. And yet the authors of this article have discovered a surprisingly large number of insignificant results in articles from established nonprofit journals. Insignificant hypotheses and Type II errors surely account for a number of these results, but the authors believe the majority of these results are due to a different cause, one that is detectable and preventable: multicollinearity.Dans les articles sur les organismes sans but lucratif, les modèles linéaires sont les outils analytiques les plus communément utilisés. En effet, académiques et praticiens utilisent tous les deux ces modèles pour évaluer diverses hypothèses relatives à leurs recherches, espérant trouver des résultats significatifs pouvant confirmer leurs théories. Pourtant, les auteurs de cet article ont découvert un nombre surprenant de résultats non significatifs dans des articles de revues établies sur les organismes sans but lucratif. Des hypothèses non significatives et des erreurs du type II expliquent sûrement certains de ces résultats, mais les auteurs croient que la majorité des résultats ont une cause différente qui est détectable et évitable : la multicolinéarité.

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