Development Of Multiple Linear Regression Models Research Articles

Three-Hour-Ahead of Multiple Linear Regression (MLR) Models for Particulate Matter (PM10) Forecasting

The increase of air pollutants emission through anthropogenic activities and natural phenomena in the atmosphere can give an adverse impact on human health especially to some groups of people such as children, the elderly, and people that have cardiovascular problems. Multiple Linear Regression (MLR) model establishments for the particulate matter (PM10) forecasting can be useful, as it provides early warning information to the local authorities and the communities. We aim to develop MLR models for PM10 forecasting in Peninsular Malaysia, specifically in the southern part. In this study, the hourly data of PM10, meteorological factors, and gaseous pollutants from the year 2009-2011 had been used. As a result, the next first hour of the MLR prediction model, PM10,t+1 has been selected as the best-fitted model as compared to the second and third prediction hour models, PM10,t+2, and PM10,t+3, respectively. The PM10,t+1 model was explained 61.4% (R2=0.614) variance in the data which is higher compared to model PM10,t+2 and PM10,t+3 with 42.3% (R2=0.423) and 34.7% (R2=0.347), respectively. Thus, the validation of PM10, t+1 model also has a high accuracy value of R2 (55.1%) as compared to the other two models. We conclude that the development of MLR models is adequate for PM10 forecasting in the industrial area.

Predictions of chromatographic retention indices of alkylphenols with support vector machines and multiple linear regression

In this study, quantitative structure-retention relationship (QSRR) was used for the prediction of Kováts retention indices of 180 alkylphenols and their derivatives using the multiple linear regression (MLR) and support vector machine (SVM). After the calculation of some molecular descriptors for all molecules, the data set was randomly divided into training and test sets. The diversity of training and test sets was examined by molecular diversity validation test. Then stepwise MLR was used for the selection of the most important descriptors and development of MLR models. Descriptors which appeared in these QSRR models are number of H atoms, relative number of O atoms, Balaban index, relation yz-shadow/yz-rectangle and partial charges hydrogen bond donor atoms HDCA(2) index. These descriptors were used as inputs for developing the SVM model. After optimizing the SVM parameters, it was used for the calculation of chromatographic retention of interest molecules. The values of SE in calculation of Kováts retention indices for training and test sets are 0.34 and 0.63, respectively, for MLR model and 0.35 and 0.63, respectively, for SVM model. The overall values of average absolute relative error were 13.24 and 13.83 for MLR and SVM models, respectively. In addition, the cross-validation tests were performed to further examine the obtained model. The calculated values of cross-validation correlation coefficient (Q(2)) and standard deviation based on predicted residual sum of square are 0.896 and 0.680 for MLR model and 0.893 and 0.67 for SVM model. These values and other obtained statistical parameters for these models reveal the suitability of QSRR in prediction of Kováts retention indices of alkylphenols using MLR and SVM techniques.