Regression Models For Response Variables Research Articles

The Maxwell-Boltzmann-Exponential distribution with regression model

Abstract This paper proposes a new probability model called as Maxwell-Boltzmann-Exponential (MBE) distribution. The MBE distribution arises as a mixture distribution of the Maxwell-Boltzmann and exponential distributions. The statistical properties of the distributions are studied and obtained in closed-form expressions. Three methodologies are assessed and compared for the estimation of parameters in the MBE distribution. The MBE regression model is defined, with the proposed regression model being an alternative to the gamma regression model for response variables that are extremely right-skewed and bimodal. Two real data sets are used to demonstrate the applicability of the proposed models against the existing models.

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications.

In this paper, we propose and derive a new regression model for response variables defined on the open unit interval. By reparameterizing the unit generalized half-normal distribution, we get the interpretation of its location parameter as being a quantile of the distribution. In addition, we can evaluate effects of the explanatory variables in the conditional quantiles of the response variable as an alternative to the Kumaraswamy quantile regression model. The suitability of our proposal is demonstrated with two simulated examples and two real applications. For such data sets, the obtained fits of the proposed regression model are compared with that provided by a Kumaraswamy regression model.

The Improvement of Yield in Formaldehyde Process

Various factors influence the efficacy of formaldehyde production. In this study, response surface methodology was applied for optimization of process parameters on the response variable (yield of formaldehyde production: Y) by a central composite design (CCD). Factors studied are the reaction temperature (X1 = 640-660 °C), mole ratio of methanol to oxygen (X2 = 2.34-2.38), mole ratio of steam to methanol (X3 = 0.90-1.10), reaction time (X4 = 22-26 millisecond; ms), and air inlet temperature (X5 = 25-30°C). As a result of CCD evaluation, the predicted quadratic regression model for response variables was significant (p < 0.05). Further 0.9745 R2 values indicated satisfactory fit of the model. In addition, the 3-D response surface and the contour plots derived the obtained model were applied to determine the optimal conditions. The optimum conditions were as follows: X1 = 660 °C, X2 =2.38, X3 = 1.10, X4 = 23.90 ms and X5= 30 °C. Corresponding to these conditions, the experimental response value (yields of formaldehyde production) agreed closely with the predicted yields of 88.61%.

Influence of the Yarn Formation Process on the Characteristics of Viscose Fabric Made of Vortex Coloured Spun Yarns

In this study, based on the Box-Behnken design, regression statistical analysis is introduced to evaluate the influence of yarn formation process variables (nozzle pressure, yarn delivery speed and yarn count) on the properties (breaking strength, air permeability rate, dynamic drape coefficient and mass loss rate) of viscose fabric fabricated from vortex colored spun yarns. Quadratic regression models for response variables affected by different combinations of model items are given. Research results show that the air permeability rate and dynamic drape coefficient for viscose fabric decreases with an increase in the yarn delivery speed from 320 to 380 m/min, while the fabric mass loss rate and fabric breaking strength are less affected by the yarn delivery speed. The mass loss rate of viscose fabric increases, reaches a peak, and then decreases with increasing nozzle pressure, while its dynamic drape coefficient, affected by the nozzle pressure, takes on the opposite trend. However, nozzle pressure has less significant effects on fabric breaking strength and fabric air perme ability. The air permeability rate and mass loss rate of viscose fabric increases firstly and then decreases with a decreasing yarn count, while the effect of yarn count on the fabric breaking strength and dynamic drape coefficient exhibits an opposite trend. Decreasing the yarn count makes the fabric dynamic drape coefficient drop firstly and then augment.

Optimization and validation of a HPLC method for simultaneous determination of aflatoxin B1, B2, G1, G2, ochratoxin A and zearalenone using an experimental design

A reversed-phase HPLC optimization strategy is presented for investigating the separation and retention behavior of aflatoxin B1, B2, G1, G2, ochratoxin A and zearalenone, simultaneously. A fractional factorial design (FFD) was used to screen the significance effect of seven independent variables on chromatographic responses. The independent variables used were: (X1) column oven temperature (20–40°C), (X2) flow rate (0.8–1.2 ml/min), (X3) acid concentration in aqueous phase (0–2%), (X4) organic solvent percentage at the beginning (40–50%), and (X5) at the end (50–60%) of the gradient mobile phase, as well as (X6) ratio of methanol/acetonitrile at the beginning (1–4) and (X7) at the end (0–1) of gradient mobile phase. Responses of chromatographic analysis were resolution of mycotoxin peaks and HPLC run time. A central composite design (CCD) using response surface methodology (RSM) was then carried out for optimization of the most significant factors by multiple regression models for response variables. The proposed optimal method using 40°C oven temperature, 1 ml/min flow rate, 0.1% acetic acid concentration in aqueous phase, 41% organic phase (beginning), 60% organic phase (end), 1.92 ratio of methanol to acetonitrile (beginning) and 0.2 ratio (end) for X1–X7, respectively, showed good prediction ability between the experimental data and predictive values throughout the studied parameter space. Finally, the optimized method was validated by measuring the linearity, sensitivity, accuracy and precision parameters, and has been applied successfully to the analysis of spiked cereal samples.