Narrow Results

This paper deals with a regression model for light weight and crashworthiness enhancement design of automotive parts in frontal car crash. The ULSAB-AVC model is employed for the crash analysis and effective parts are selected based on the amount of energy absorption during the crash behavior. Finite element analyses are carried out for designated design cases in order to investigate the crashworthiness and weight according to the material and thickness of main energy absorption parts. Based on simulations results, a regression analysis is performed to construct a regression model utilized for light weight and crashworthiness enhancement design of automotive parts. An example for weight reduction of main energy absorption parts demonstrates the validity of a regression model constructed.

A new method based on eye-tracking data — visual momentum (VM) — was introduced to quantitatively evaluate a dynamic interactive visualization interface. We extracted the dimensionless factors from the raw eye-tracking data, including the fixation time factor $T$, the saccade amplitude factor D and the fixation number factor $N$. A predictive regression model of VM was deduced by eye movement factors and the performance response time (RT). In Experiment 1, the experimental visualization materials were designed with six effectiveness levels according to design techniques proposed by Woods to improve VM (total replacement, fixed format data replacement, long shot, perceptual landmark and spatial representation) and were tested in six parallel subject groups. The coefficients of the regression model were calculated from the data of 42 valid subjects in Experiment 1. The mean VM of each group exhibited an increasing trend with an increase in design techniques. The data of the performance and eye tracking among the combined high VM group, middle VM group and low VM group indicated significant differences. The data analysis indicates that the results were consistent with the previous qualitative research of VM. We tested and verified this regression model in Experiment 2 with another dynamic interactive visualization. The results indicated that the VM calculated by the regression model was significantly correlated with the performance data. Therefore, the virtual parameter VM can be a quantitative indicator for evaluating dynamic visualization. It could be a useful evaluation method for the dynamic visualization in general working environments.

In an already classical paper, May [1976] pointed out that simple nonlinear models in ecology can possess complicated dynamics. A long debate concerning the possible existence of chaotic ecologies has followed the appearance of this paper. Morris [1990] stressed that several problems exist when making conclusions regarding chaotic or nonchaotic dynamics as models are fitted to ecological data. Takens' theorem [1981] should, in principle, provide tools for solving some of these problems, but in reality essential assertions are most often violated. First, limits regarding the length of the used time-series must be assumed. Second, the theorem can be applied for evaluating positive Lyapunov exponents only, and is hence not applicable for distinguishing nonchaotic dynamics from chaotic.

We use a deterministic food-chain model that possesses a wide range of different dynamical patterns to demonstrate the existence of cases that are misclassified with respect to chaotic or nonchaotic motion as models are fitted to data in the various dynamical regimes. Our results are valid regardless of what finite data size is assumed. The results are best understood for high-periodic cases in the noise-free limit. If the relevant phase-space is not sufficiently well-populated with data in the vicinity of the periodic orbit, then sufficient complexity of the models are not supported by standard model selection criteria like AIC or GCV. Thus, the fitted models only in the best cases contain information concerning both the location of the periodic orbit and the eigenvalues of the Jacobians evaluated along the periodic orbit. If the space is moderately well populated with data, then the data is often described by an unstable periodic orbit of the fitted model. The attractor that was to be described by the fitted model was destabilized and is now a repeller. We call this phenomenon stability switches. It reminds about the noise-induced phenomenon reported by Rand and Wilson [1992], but we point out that the problem reported here is caused by the fitting procedure itself, not by the added noise.

The repeller that has been created by the model-fitting procedure can be located in the basins of attraction of some fixed point, the infinity, or some periodic or chaotic attractors of the fitted models. The situation seems similar when periodic attractors are not well enough populated with data for describing their location and when chaotic attractors are to be described by data. Similar stability switches occur and the dynamics of models fitted to data may differ or coincide with the dynamics of the attractor that generated the data in an unpredictable manner.

A person’s preference to select or reject certain meals is influenced by several aspects, including colour. In this paper, we study the relevance of food colour for such preferences. To this end, a set of images of meals is processed by an automatic method that associates mood adjectives that capture such meal preferences. These adjectives are obtained by analyzing the colour palettes in the image, using a method based in Kobayashi’s model of harmonic colour combinations. The paper also validates that the colour palettes calculated for each image are harmonic by developing a rating model to predict how much a user would like the colour palettes obtained. This rating is computed using a regression model based on the COLOURlovers dataset implemented to learn users’ preferences. Finally, the adjectives associated automatically with images of dishes are validated by a survey which was responded by 178 people and demonstrates that the labels are adequate. The results obtained in this paper have applications in tourism marketing, to help in the design of marketing multimedia material, especially for promoting restaurants and gastronomic destinations.

A new approach to the regression models analysis has been presented. It is based on the use of the Generalized Law of Reliability and a method allowing one to transform initial lifetime data to fit a model of accelerated tests. A model of the accelerated tests and regression models of both lung cancer and leukemia trails have been considered.

The paper considers the Bayesian analysis of an elaborated family of regression models based on the inverse Gaussian distribution, a family that is quite useful for the accelerated test scenario in life testing. A variety of relationships between the model parameters and the entertained stress variable gives rise to four different families. For the Bayesian implementation, the paper considers independent weak priors for the parameters and proposes Gibbs sampler algorithm for obtaining samples from the relevant posteriors. The implementation is also extended when the data are subject to censoring mechanism. Numerical illustration is based on a real dataset on temperature accelerated life testing. Finally, the compatibility of each entertained model is assessed and they are compared using some commonly available Bayesian toolkits. The results are found to be satisfactory.

Current paper comprises the inter-relationship between second-order regression modeling and genetic algorithm (GA)-based optimization of air plasma deposited with improved thermal barrier coating (TBC) systems structures. For developing the regression model, experiments were performed as per $L_{27}$ orthogonal array, and models were established by MINITAB software. The regression models have been found satisfactory for predicting the responses at 99% confidence level. GA optimization showed a 14.86% improvement in hardness and a 15.99% reduction in roughness. The optimal level of air plasma spraying (APS) parameters was obtained as 8 number of spraying layers, 70V of accelerating voltage, 600A of Arc current, 30mm/s of travel speed, 100mm of spray distance, 25g/min of powder feed rate, 4J/min of carrier gas flow rate, and 55L/min of primary gas flow rate for maximum hardness and minimum roughness.

This paper performed some exploratory data visualization on this data set. The nature and representation of input data was found out and the preliminary feature selection was conducted in this step. And this paper performed data preprocessing and feature engineering on this data set, which had critical importance of the accuracy of prediction results. The paper built multiple regression models on the missing values prediction in the testing set. The paper implemented various data mining algorithms to build predictive models, including Gaussian Naive Bayes classifier, K-Nearest Neighbors (K-NN) algorithm, Multi-layer Perceptron (MLP), Logistic regression, random forest and XGBoost. After the experiments, XGBoost classifier could give the best result among all the models.

This study presented optimal estimation of total plantar force with a suitable sensor layout and a reliable equation for monitoring gait in daily life activities. The plantar pressure of 10 subjects during level walking was measured by Pedar^® insoles at 100 Hz for establishing models and selecting the optimal one. Four types of virtual sensors with different sizes were designed. Stepwise linear regressions were performed to reconstruct total plantar force based on each particular type of virtual sensor. 14 models were established, which met the requirements of the explained variance of the regression model and the multicollinearity of the predictors. Estimated total plantar force from each model was compared with the real data from the Pedar^® insoles. According to the correlation coefficient (R) and the root mean square error divided by the peak force (RMSE/PF), the optimal model had three sensors located under the heel and metatarsal. Another four subjects were used for validating the optimal model by performing level walking, running, vertical jump-landing, stair ascending and descending. For these five common activities, the correlation was high (R > 0.970) and the error was low (RMSE/PF < 10%). Therefore, this model can accurately estimate total plantar force in daily life activities.

The lower limb rehabilitation process requires external control inputs based on joint kinematics and kinetics to its actuator for generating the motion of a robotic assistive device. This paper describes the procedures for measuring, predicting and validating the joint kinematics and kinetics of human gait for the lower limb exoskeleton. The high-speed multi-camera-based video system associated with passive optical markers and a force plate sensor is used to measure the gait data. The lower limb joint torques have also been predicted using three different machine learning regression models, viz. Decision Tree (DT), Gaussian Process Regression (GPR) and Support Vector Machine (SVM). The analysis is further validated with the geometry-based analytical method. Three lower limb joint torques have been predicted by utilizing gait period, joint angle, joint velocity and joint acceleration as the predictors. The lowest average 10-fold cross-validation Root Mean Square Error (RMSE) using the DT model between measured and predicted torques have been recorded for the ankle, knee and hip joint as 1.9521, 1.5527 and 1.5684Nm, respectively. This study enhances the field of medical rehabilitation by providing the required knowledge of human gait kinematics/kinetics and predicting the joint torque profile without any force sensor.

Estimations and optimal experimental designs for two-dimensional Haar-wavelet regression models are discussed. It is shown that the eigenvalues of the covariance matrix of the best linear unbiased estimator of the unknown parameters in a two-dimensional linear Haar-wavelet model can be represented in closed form. Some common discrete optimal designs for the model are constructed analytically from the eigenvalues. Some equivalences among these optimal designs are also given, and an example is demonstrated.

Protein-protein binding interaction is the most prevalent biological activity that mediates a great variety of biological processes. The increasing availability of experimental data of protein–protein interaction allows a systematic construction of protein–protein interaction networks, significantly contributing to a better understanding of protein functions and their roles in cellular pathways and human diseases. Compared to well-established classification for protein–protein interactions (PPIs), limited work has been conducted for estimating protein–protein binding free energy, which can provide informative real-value regression models for characterizing the protein–protein binding affinity. In this study, we propose a novel ensemble computational framework, termed ProBAPred (Protein–protein Binding Affinity Predictor), for quantitative estimation of protein–protein binding affinity. A large number of sequence and structural features, including physical–chemical properties, binding energy and conformation annotations, were collected and calculated from currently available protein binding complex datasets and the literature. Feature selection based on the WEKA package was performed to identify and characterize the most informative and contributing feature subsets. Experiments on the independent test showed that our ensemble method achieved the lowest Mean Absolute Error (MAE; 1.657kcal/mol) and the second highest correlation coefficient ($R\text{-value}=0.467$), compared with the existing methods. The datasets and source codes of ProBAPred, and the supplementary materials in this study can be downloaded at http://lightning.med.monash.edu/probapred/ for academic use. We anticipate that the developed ProBAPred regression models can facilitate computational characterization and experimental studies of protein–protein binding affinity.

In this paper, we introduce a modified family of distributions that unifies three different families with only one tuning parameter; the so-called exp-$G$, Topp–Leone-$G$ and exp-half-$G$ families of distributions. We study mathematical properties of the proposed family, including linear representations, quantile function, probability weighted moments, reliability parameter and stochastic ordering. One of the corresponding parametric statistical model is outlined, with estimation of the parameters by the method of maximum likelihood and investigation for possible applications to glycosaminoglycans concentration level in urine over the beta Weibull and Kumaraswamy Weibull distributions. The goodness-of-fit of five other members of the family is also assessed. Regression model is also discussed using the proposed distribution and applied to establish the relationship between the glycosaminoglycans concentration level and age of the children.

Total green leaf area (GLA) is an important trait for agronomic studies. However, existing methods for estimating the GLA of individual rice plants are destructive and labor-intensive. A nondestructive method for estimating the total GLA of individual rice plants based on multi-angle color images is presented. Using projected areas of the plant in images, linear, quadratic, exponential and power regression models for estimating total GLA were evaluated. Tests demonstrated that the side-view projected area had a stronger relationship with the actual total leaf area than the top-projected area. And power models fit better than other models. In addition, the use of multiple side-view images was an efficient method for reducing the estimation error. The inclusion of the top-view projected area as a second predictor provided only a slight improvement of the total leaf area estimation. When the projected areas from multi-angle images were used, the estimated leaf area (ELA) using the power model and the actual leaf area had a high correlation coefficient (R² > 0.98), and the mean absolute percentage error (MAPE) was about 6%. The method was capable of estimating the total leaf area in a nondestructive, accurate and efficient manner, and it may be used for monitoring rice plant growth.

Energy consumption and its associated consequences can be reduced by implementing district cooling strategies that supply low temperature water to a wide range of end users through chillers and distribution networks. Adequate understanding, performance prediction and further optimization of vapor compression chillers used widely in district cooling plants have been a subject of intense research through model-based approaches. In this context, we perform an extensive review of different modeling techniques used for predicting steady-state or dynamic performance of vapor compression liquid chillers. The explored modeling techniques include physical and empirical models. Different physical models used for vapor compression chillers, based on physics laws, are discussed in detail. Furthermore, empirical models (based on artificial neural networks, regression analysis) are elaborated along with their advantages and drawbacks. The physical models can depict both steady- and unsteady-state performance of the vapor compression chiller; however, their accuracy and physical realism can be enhanced by considering the geometrical arrangement of the condenser and evaporator and validating them for various ecofriendly refrigerants and large system size (i.e., cooling capacity). Apparently, empirical models are easy to develop but do not provide the necessary physical realism of the process of vapor compression chiller. It is further observed that DC plants/networks have been modeled from the point of view of optimization or integration but no efforts have been made to model the chillers with multiple VCR cycles. The development of such models will facilitate to optimize the DC plant and provide improved control strategies for effective and efficient operation.

Water scarcity is an alarming issue in the developing world. Due to population explosion, the supply of water to households is becoming difficult. And as the quality of water supply infrastructure is deteriorating, clean water is getting mixed with sewage and becoming a cause of waterborne diseases. This study was carried out in the city of Lahore, Pakistan, to find out the willingness to pay (WTP) for improved water supply by using Contingent Valuation Method (CVM). This study explores the relationship of WTP with socio-economic factors, i.e. income, accommodation and employment. Moreover, questionnaires were administered to randomly selected 200 respondents. For statistical analysis stepwise linear regression, Pearson correlation and chi square were employed to find out the variables that determine WTP for improved water supply quality. Results showed that income was the variable that most significantly impacted the WTP for improved water supply. The WTP amount was found to be 0.70 USD. People were not generally satisfied with the water supply quality. Unavailability of water for 1–2h per day was commonly reported by the respondents. However, more studies should be conducted with a larger sample size to enhance our knowledge about water supply situation in Lahore.

In several applications, the distribution of the data is frequently unimodal, asymmetric or bimodal. The regression models commonly used for applications to data with real support are the normal, skew normal, beta normal and gamma normal, among others. We define a new regression model based on the odd log-logistic geometric normal distribution for modeling asymmetric or bimodal data with support in $ℝ$, which generalizes some known regression models including the widely known heteroscedastic linear regression. We adopt the maximum likelihood method for estimating the model parameters and define diagnostic measures to detect influential observations. For some parameter settings, sample sizes and different systematic structures, various simulations are performed to verify the adequacy of the estimators of the model parameters. The empirical distribution of the quantile residuals is investigated and compared with the standard normal distribution. We prove empirically the usefulness of the proposed models by means of three applications to real data.

Radial Basis Function Neural Networks (RBF NN) are frequently used for learning the rule of complex phenomenon and system. But kernel matrix computation for high dimensional data source demands heavy computing power. To shorten the computing time, the paper designs a parallel algorithm to compute the kernel function matrix of RBF NN and applies it to the prediction of converter re-vanadium modeling. This paper studies the possibility of using parallel kernel RBF regression for modeling an intelligent decision system for re-vanadium in metallurgical process. The paper then implements the algorithm on a cluster of computing workstations using MPI. Finally, we experiment with the practical data to study the speedups and accuracy of the algorithm. The proposed algorithm proves to be effective and practicable in its application.

In this paper the regression models used for description and forecasting of the inland rail passenger conveyances of the regions of Latvia were considered. Two estimation approaches were compared: the classical linear regression model and the single index model. Various tests for hypothesis of explanatory variables insignificance and model correctness have been lead, and the cross-validation approach has been carried out as well. The analysis has shown obvious preference of the single index model.

The following sections are included:

• INTRODUCTION

• POPULATION PARAMETERS AND THE REGRESSION MODELS
  • Data Description
  • Building the Population Regression Model
  • Sample Versus Population Regression Model

• THE LEAST-SQUARES ESTIMATION OF α AND β
  • Scatter Diagram
  • The Method of Least Squares
  • Estimation of Intercept and Slope

• STANDARD ASSUMPTIONS FOR LINEAR REGRESSION

• THE STANDARD ERROR OF ESTIMATE AND THE COEFFICIENT OF DETERMINATION
  • Variance Decomposition
  • Standard Error of Residuals (Estimate)
  • The Coefficient of Determination

• THE BIVARIATE NORMAL DISTRIBUTION AND CORRELATION ANALYSIS
  • The Sample Correlation Coefficient
  • The Relationship Between r and b
  • The Relationship Between r and R²

• Summary

• Appendix 13A Derivation of Normal Equations and Optimal Portfolio Weights

• Appendix 13B The Derivation of Equation 13.16

• Appendix 13C The Bivariate Normal Density Function
  • Using a Mathematics Aptitude Test to Predict Grade in Statistics

• Appendix 13D American Call Option and the Bivariate Normal CDF
  • Valuating American Option

• Questions and Problems