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Modeling the Resilient Modulus of Soils
Published in A. Gomes Correia, Fernando E.F. Branco, Bearing Capacity of Roads, Railways and Airfields, 2020
B. Ni, T.C. Hopkins, L. Sun, T.L. Beckham
To evaluate the five models described herein, 60 resilient modulus tests were performed on clayey specimens to generate data for correlation analysis. Results of simple correlation analysis using three confining stresses show that a wide range of coefficients may be obtained for the four published models. The model suggested by the authors yield fairly uniform correlation coefficients when simple regression analysis is performed on data for a selected confining stress. For a given confining stress, the coefficients of all models yield reasonable results. However, only the models proposed by Uzan and the authors relate the resilient modulus to the confining stress and deviator collectively. Multiple correlation analysis show that both models yield good results in the domain of testing stresses. The coefficient of multiple correlation of the authors’ model is slightly better than the coefficient of multiple correlation obtained for Uzan’s model. However, the resilient modulus computed from Uzan’s model approaches infinity as the stresses approach zero. The model proposed by the authors does not diverge at small stresses, provides a good relationship between resilient modulus and stresses in the domain of testing stresses, and appears to provide a reasonable relationship for any given stress state.
The Flood Hydrograph
Published in Richard J. Chorley, Introduction to Physical Hydrology, 2019
Slope, like elevation, is an obvious control of peak discharge, but again it is a factor which is difficult to interpret meaningfully. Some methods of slope assessment are extremely involved and require measurement of length of all contours in a basin, or counting the number of intersections between contours and a grid overlay. Others are relatively simple, but the importance of these basin slope indices has been difficult to establish, whereas measurements of channel slope have been proved significant. One slope index (S) devised for a study of fifty-seven British drainage basins showed little significance, even when log S was correlated with log Qm. However, when slope was combined with basin area, as below, a coefficient of multiple correlation of +0.93 resulted:
Advanced Forecasting and Inventory Modeling
Published in Adedeji B. Badiru, Project Management, 2019
The coefficient of multiple correlation is defined as the positive square root of R2. That is, R=R2
Spatiotemporal dynamics of population density in China using nighttime light and geographic weighted regression method*
Published in International Journal of Digital Earth, 2023
Wei Guo, Jinke Liu, Xuesheng Zhao, Wei Hou, Yunxuan Zhao, Yongxing Li, Wenbin Sun, Deqin Fan
Before conducting linear regression model, it is crucial to perform multicollinearity analysis on the characteristic variable. When severe multicollinearity exists, the independent variables are interdependent and vary with each other, which leads to the inability to obtain the true relationship between the independent and dependent variables. Therefore, before conducting geographically weighted regression model, we use the variance inflation factor (VIF) to test multicollinearity issues of the characteristic variables (O’brien 2007). The VIF depicts the degree of linear correlation between each variable. It is generally believed that when the VIF is greater than 10, there is a multicollinearity problem. where, .represents the coefficient of multiple correlation when one independent variable is regressed against the other independent variables. The tolerance is calculated as , which is inversely proportional to VIF.
Modelling the complexity of the foot and ankle during human locomotion: the development and validation of a multi-segment foot model using biplanar videoradiography
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Jayishni N. Maharaj, Michael J. Rainbow, Andrew G. Cresswell, Sarah Kessler, Nicolai Konow, Dominic Gehring, Glen A. Lichtwark
For statistical analysis, each trial was cropped to the period of time when there was tracked BVR data for all participants (11–80% of the stance phase). This ensured that the same period of the stance phase was assessed across all participants. Relative motion of the midtarsal (midfoot–calcaneus) and tarsometatarsal (forefoot–midfoot) joints were assessed in the sagittal plane only due to uncertanities in BVR data. The congruity of models with BVR, at all joints and planes, was compared using the coefficient of multiple correlation (CMC). CMC scores range between 0 and 1 and can be stratified as: poor similarity (0–0.60); moderate (0.60–0.75); good (0.75–0.85); very good (0.85–0.95) and excellent (0.95–1). Root mean square (RMS) differences were calculated to assess the differences in magnitudes across stance. The mean RMS differences across stance for each subject and joint were subsequently compared between models using a paired t test.
Analysis and evaluation of the systems used for the assessment of the cervical spine function: a systematic review
Published in Journal of Medical Engineering & Technology, 2021
Paola A. Vásquez-Ucho, Gandhi F. Villalba-Meneses, Kevin O. Pila-Varela, Carlos P. Villalba-Meneses, Iván Iglesias, Diego A. Almeida-Galárraga
In the research of accuracy and test-retest repeatability of different systems or tools studied, several techniques are employed to analyse resulting data such as the intraclass correlation coefficient (ICC), multiple correlation coefficient (MCC), Pearson correlation coefficient (PCC), coefficient of variation (CV), coefficient of determination (R2), limits of agreement (LOA), for angular discrepancies. Additionally, to obtain the differences between the results of two devices, formulas employed are mean squared error (MSE), root mean square error (RMSE), and standard error of the mean (SEM), which is used to define the error extension and from which the minimal detectable change (MDC) can be obtained too. Among the graphical methods, authors use Bland-Altman graphics to show graphical differences between the two system’s results and verify the agreement between them, scatter diagrams, linear regressions, and T-test. All the mentioned formulas are employed to validate and test the reliability and accuracy of the systems for the cervical spine assessment. That is to say, once the resulting values of the studies are obtained, authors rely on these data analysis techniques, which allow them to present sustainable conclusions about the utility and validity of a specific system in comparison to the commercially available and commonly used.