Developed Multiple Linear Regression Models Research Articles

Modeling and mechanistic understanding of cytotoxicity of metal oxide nanoparticles (MeOxNPs) to Escherichia coli: categorization and data gap filling for untested metal oxides

Metal oxide nanoparticles (MeOxNPs) production is expected to increase every year exponentially, and their potential to cause adverse effect to the environment and human health will also expand rapidly. Hence, risk assessment of nanoparticles (NPs) is necessary to design ecosafe products. However, experimental ecotoxicological assessments are time-consuming requiring a lot of resources. Therefore, researchers rely on alternative in silico approaches to predict the behavior of NPs in the biological system. Quantitative structure − toxicity relationship (QSTR) has been adopted as a potential method to predict the cytotoxicity of untested NPs. Hence, in the present study, multiple linear regression (MLR) models were developed using 17 MeOxNPs on Escherichia coli (E. coli) bacteria cells under both light and dark conditions. The models were developed applying Small Dataset Modeler software, version 1.0.0 (http://teqip.jdvu.ac.in/QSAR_Tools/DTCLab/) which generates models with a limited number of data points. Periodic table-based descriptors (both 1st and 2nd generation) were used for the modeling purpose. Two statistically significant MLR models based on photo-induced toxicity ( R 2 = 0.726) and dark-based toxicity ( R 2 = 0.770) were developed. From the developed models, we interpreted that increase in valency and oxidation state of the metal will decrease the cytotoxicity whereas the atomic radius of the metal and electronegativity of MeOxNPs influence the toxicity toward E. coli cells. The MLR models were validated using different internal validation metrics. Additionally, we have collected 42 MeOxNPs as an external set to observe the predictive power of the two developed MLR models and categorize them into toxic and non-toxic classes. The chemical features selected in the developed models are important for understanding the mechanisms of nanotoxicity. Thus, the developed models can be a scientific basis for designing safer NPs.

Evaluating multiple predictive models for beach management at a freshwater beach in the Great Lakes region

Recreational water quality is currently monitored at Sandpoint Beach on Lake St. Clair using culture-based enumeration of Escherichia coli. Using water quality and weather data collected over 4 yr, several multiple linear regression (MLR)-based models were developed for near real-time prediction of E. coli concentration and were tested using independent data from the fifth year. Model performance was assessed by the determination of metrics such as RMSE, accuracy, specificity, sensitivity, and area under the receiver operating characteristic curve (AUROC). Each of the developed MLR models described herein resulted in increased correct responses for both exceedance and non-exceedance of the applicable standard as compared to predictions based on E. coli measurements (persistence models, using the previous day's E. coli concentration), which is the method currently being used. The AUROC values for persistence models are between 0.5 and 0.6, as compared to >0.7 for all the MLR models described herein. Among the MLR models, model performance improved when qualitative sky weather condition, which is commonly reported but was not previously used in similar models, was included. To select the best model, a principal coordinate analysis was used to combine multiple model performance metrics and provide a more sensitive tool for model comparison. Although models developed using 2, 3, and 4 yr of monitoring data provided reasonable performance, the model developed using the most recent 2-yr data was marginally better. Thus, data from the most recent 2 yr are likely sufficient as a training dataset for updating the MLR model for Sandpoint Beach in the future.

Quality by Design Approach Using Multiple Linear and Logistic Regression Modeling Enables Microemulsion Scale Up.

The development of pharmaceutical nanoformulations has accelerated over the past decade. However, the nano-sized drug carriers continue to meet substantial regulatory and clinical translation challenges. In order to address some of these key challenges in early development, we adopted a quality by design approach to develop robust predictive mathematical models for microemulsion formulation, manufacturing, and scale-up. The presented approach combined risk management, design of experiments, multiple linear regression (MLR), and logistic regression to identify a design space in which microemulsion colloidal properties were dependent solely upon microemulsion composition, thus facilitating scale-up operations. Developed MLR models predicted microemulsion diameter, polydispersity index (PDI), and diameter change over 30 days storage, while logistic regression models predicted the probability of a microemulsion passing quality control testing. A stable microemulsion formulation was identified and successfully scaled up tenfold to 1L without impacting droplet diameter, PDI, or stability.

PREDICTION THE AVERAGE ANNUAL CONCENTRATION OF PHOSPHATE IN RIVERS USING ANN AND MLR MODELS

Clean and quality water is one of the main aims in achieving the seventeen adopted Sustainable Development Goals. That means taking legislative measures at national and international level for the preservation of water quality, prevention of pollution and continuous monitoring. According to global and regional cooperation which is stated by numerous legal regulations, all member countries have obligation to monitoring water quality and submit annual report. For that reason it is very important to obtain accurate and precise data of all monitored water pollutants. In developing countries, because of poor and underdeveloped environmental infrastructure, obtained data for pollutants could have a certain percentage of uncertainty. In order to avoid that problem it is very important the existence of a larger number of models to estimate concentration of water pollutants, including concentration of phosphate. Due to the increasing influence of anthropogenic sources on the content of phosphorus, first in the soil and then in water sources, and negative effects caused by the eutrophication process, it is crucial to monitor the state of water in terms of the presence of phosphate. In the present study, in order to obtain one optimal model to predict the average annual concentration of phosphate in rivers was used two different approaches. In the first approach, was used artificial neural network (ANN), two different ANN architecture: Multilayer Perceptron (MLP) and Radial Basis Function (RBF). In the second approach were used two type of Multiple Linear Regression (MLR) technique, simultaneous and stepwise MLR. Available data used in this study were obtained from Eurostat-the statistical office of the European Union, for 19 European countries for the period from 2004 to 2012. For all created models was used the same dataset. As input variables were used sustainable development indicators, in total 10. All selected inputs were chosen on the basis of their influence on phosphate concentration in rivers and also reviewing of adequate literature. As model performance indicators in this study was used Mean Absolute Error (MAE) and coefficient of determination (R2). Results of all created models first at all showed that comparing two ANN models, better performances on training and test dataset shows MLP model. On test dataset, MLP model gives satisfactory prediction with value of coefficient of determination 0,657. On the other side, developed MLR models show significantly poorer results. Taking into account performances of created models, it is clearly that MLP model shows the best predictive results. On the basis of results of MLP model, could be recognized that it can be an alternative model for prediction annual concentration of phosphate in rivers, and significant tool in water pollutant monitoring.

Prediction of Sitophilus granarius infestation in stored wheat grain using multivariate chemometrics & fuzzy logic-based electronic nose analysis

Insect infestation is an alarming concern in stored wheat grain, accounting for losses in quality as well as quantity. Infested wheat with Sitophilus granarius for four different storage periods with various degrees of infestation were evaluated through E-nose. A fuzzy logic based approach was undertaken to screen the relatively more sensitive sensors towards infestation. Multiple linear regression (MLR) models were further used to predict the uric acid and protein content as infestation indices. Principal component analysis (PCA) and hierarchical cluster analysis (HCA) efficiently classified the most infested wheat grain samples among the stored samples. The developed MLR models were found best fit with higher regression co-efficient (R2) value and lower root mean square error (RMSE). The E-nose sensor responses closely predicted the uric acid (R2 = 0.958; RMSE = 1.401) and protein content (R2 = 0.978; RMSE = 0.275). The findings of this study will open up a convenient, rapid yet nondestructive approach for quality determination of insect infested wheat grains at various stages during the storage.

Multiple linear regression modelling of on-farm direct water and electricity consumption on pasture based dairy farms

An analysis into the impact of milk production, stock numbers, infrastructural equipment, managerial procedures and environmental conditions on dairy farm electricity and water consumption using multiple linear regression (MLR) modelling was carried out. Electricity and water consumption data were attained through the utilisation of a remote monitoring system installed on a study sample of 58 pasture-based, Irish commercial dairy farms between 2014 and 2016. In total, 15 and 20 dairy farm variables were analysed on their ability to predict monthly electricity and water consumption, respectively. The subsets of variables that had the greatest prediction accuracy on unseen electricity and water consumption data were selected by applying a univariate variable selection technique, all subsets regression and 10-fold cross validation. Overall, electricity consumption was more accurately predicted than water consumption with relative prediction error values of 26% and 49% for electricity and water, respectively. Milk production and the total number of dairy cows had the largest impact on electricity consumption while milk production, automatic parlour washing and whether winter building troughs were reported to be leaking had the largest impact on water consumption. A standardised regression analysis found that utilising ground water for pre-cooling milk increased electricity consumption by 0.11 standard deviations, while increasing water consumption by 0.06 standard deviations when recycled in an open loop system. Milk production had a large influence on model overprediction with large negative correlations of −0.90 and −0.82 between milk production and mean percentage error for electricity and water prediction, respectively. This suggested that overprediction was inflated when milk production was low and vice versa. Governing bodies, farmers and/or policy makers may use the developed MLR models to calculate the impact of Irish dairy farming on natural resources or as decision support tools to calculate potential impacts of on-farm mitigation practises.

A comprehensive investigation on static and dynamic friction coefficients of wheat grain with the adoption of statistical analysis

This paper deals with studying and modeling static friction coefficient (SFC) and dynamic friction coefficient (DFC) of wheat grain as affected by several treatments. Significance of single effect (SE) and dual interaction effect (DIE) of treatments (moisture content and contact surface) on SFC and, SE, DIE, and triple interaction effect (TIE) of treatments (moisture content, contact surface and sliding velocity) on DFC were determined using statistical analysis methods. Multiple linear regression (MLR) modeling was employed to predict SFC and DFC on different contact surfaces. Predictive ability of developed MLR models was evaluated using some statistical parameters (coefficient of determination (R2), root mean square error (RMSE), and mean relative deviation modulus (MRDM)). Results indicated that significant increasing DIE of treatments on SFC was 3.2 and 3 times greater than significant increasing SE of moisture content and contact surface, respectively. In case of DFC, the significant increasing TIE of treatments was 8.8, 3.7, and 8.9 times greater than SE of moisture content, contact surface, and sliding velocity, respectively. It was also found that the SE of contact surface on SFC was 1.1 times greater than that of moisture content and the SE of contact surface on DFC was 2.4 times greater than that of moisture content or sliding velocity. According to the reasonable average of statistical parameters (R2=0.955, RMSE=0.01788 and MRDM=3.152%), the SFC and DFC could be successfully predicted by suggested MLR models. Practically, it is recommended to apply the models for direct prediction of SFC and DFC, respective to each contact surface, based on moisture content and sliding velocity.

Modeling daily chlorophyll a dynamics in a German lowland river using artificial neural networks and multiple linear regression approaches

Phytoplankton biomass is an important indicator for water quality, and predicting its dynamics is thus regarded as one of the important issues in the domain of river ecology and management. However, the vast majority of models in river systems have focused mostly on flow prediction and water quality with very few applications to biotic parameters such as chlorophyll a (Chl a). Based on a 1.5-year measured dataset of Chl a and environmental variables, we developed two modeling approaches [artificial neural networks (ANN) and multiple linear regression (MLR)] to simulate the daily Chl a dynamics in a German lowland river. In general, the developed ANN and MLR models achieved satisfactory accuracy in predicting daily dynamics of Chl a concentrations. Although some peaks and lows were not predicted, the predicted and the observed data matched closely by the MLR model with the coefficient of determination (R 2), Nash–Sutcliffe efficiency (NS), and the root mean square error (RMSE) of 0.53, 0.53, and 2.75 for the calibration period and 0.63, 0.62, and 1.94 for the validation period, respectively. Likewise, the results of the ANN model also illustrated a good agreement between observed and predicted data during calibration and validation periods, which was demonstrated by R 2, NS, and RMSE values (0.68, 0.68, and 2.27 for the calibration period, 0.55, 0.66 and 2.12 for the validation period, respectively). According to the sensitivity analysis, Chl a concentration was highly sensitive to dissolved inorganic nitrogen, nitrate–nitrogen, autoregressive Chl a, chloride, sulfate, and total phosphorus. We concluded that it was possible to predict the daily Chl a dynamics in the German lowland river based on relevant environmental factors using either ANN or MLR models. The ANN model is well suited for solving non-linear and complex problems, while the MLR model can explicitly explore the coefficients between independent and dependent variables. Further studies are still needed to improve the accuracy of the developed models.

Biopartitioning micellar chromatography with sodium dodecyl sulfate as a pseudo α1-acid glycoprotein to the prediction of protein–drug binding

A simple and fast method is of urgent need to measure protein–drug binding affinity in order to meet the rapid development of new drugs. Biopartitioning micellar chromatography (BMC), a mode of micellar liquid chromatography (MLC) using micellar mobile phases in adequate experimental conditions, can be useful as an in vitro system in mimicking the drug–protein interactions. In this study, sodium dodecyl sulfate–micellar liquid chromatography (SDS–MLC) was used for the prediction of protein–drug binding based on the similar property of SDS micelles to α1-acid glycoprotein (AGP). The relationships between the BMC retention data of a heterogeneous set of 14 basic and neutral drugs and their plasma protein binding parameter were studied and the predictive ability of models was evaluated. Modeling of logkBMC of these compounds was established by multiple linear regression (MLR) and second-order polynomial models obtained in two different concentrations (0.07 and 0.09M) of SDS. The developed MLR models were characterized by both the descriptive and predictive ability (R2=0.882, RCV2=0.832 and R2=0.840, RCV2=0.765 for 0.07 and 0.09M SDS, respectively). The p values <0.01 also indicated that the relationships between the protein–drug binding and the logkBMC values were statistically significant at the 99% confidence level. The standard error of estimation showed the standard deviation of the regression to be 11.89 and 13.87 for 0.07 and 0.09M, respectively. The application of the developed model to a prediction set demonstrated that the model was also reliable with good predictive accuracy. The external and internal validation results showed that the predicted values were in good agreement with the experimental value.

QSAR study of selective I1-imidazoline receptor ligands

Selective imidazoline1-receptor (I1-R) ligands are used clinically to reduce blood pressure. Thus, there is significant interest in developing new imidazoline analogs with high selectivity and affinity for I1 receptors. A quantitative structure–activity relationship (QSAR) study was carried out on 11 potent I1-R ligands (derivatives of imidazoline, oxazoline and pyrroline) using a multiple linear regression (MLR) procedure. The selected compounds have been studied using B3LYP/3–21G(d, p) and B3LYP/6–31G(d, p) methods. Among the 42 descriptors that were considered in generating the QSAR model, three descriptors (partial atomic charges of nitrogen in the heterocyclic moiety (N-2 charge), log D and the dipole moment of the ligands) resulted in a statistically significant model with r 2 > 0.874 and > 0.802. The QSAR models were validated through cross-validation and external test set prediction. The aim of the developed MLR models for the I1-R ligands was to link the structures to their reported I1-R binding affinity log(1/Ki). The proposed QSAR models indicate that an increase in log D and the dipole moment value and a decrease in N-2 charge in the heterocyclic moiety are predictors of better selectivity and affinity for I1 receptors. The developed QSAR model is intended to predict the I1-R binding affinity of related compounds and aid in the rational design of new potent and selective I1-R ligands.