An Exploration of Data Prediction Based on Multiple Linear Regression Models and Bayesian Regression

Water is considered as an essential commodity in human society. It has been observed that the basic standard of living of any Country can be measure through the effective portable water supply for consumption, sanitation and hygiene for the citizen. Its production and supply in the Federal Capital Territory (FCT), Abuja, Nigeria is a challenge, as dominant percentages of lower- class workforce live outside the FCTWB existing water network, and depend on borehole or tanker for water. The demand on the water supply system in FCT, Abuja has exceeded its initial design population, and the system is incomplete and operating with only 720 million liter of water per day (MLD) functioning plant. On this basis, this study seeks to identify the best model that fit daily water supply data in FCT, Abuja and to forecast the future daily water supply in this area. The comparing models were artificial neural, multiple linear and non-linear regression model were applied to the data set of daily water production, daily water treated, daily water supply, daily water leakage, Number of household connected to Federal Capital Territory Water board water network, Number of Commercial area connected to Federal Capital Territory Water board water network, and the Estimated population of Federal Capital Territory ,Abuja from (2013 to 2020), and it was emerged that the most adequate model for the data was Multiple linear regression model (MLR), with (R2 =1.000), (RMSE = 0.00282), and (MAE = 6.540). Artificial neural network records the high value of (RMSE = 432.4321), (MAE = 549.444) and (R2 =0.921), and multiple nonlinear regression record the highest value of (RMSE = 806.687), (MAE = 666.421) and (R2 = 0.999). From the statistical measure of goodness of fit, the three models compared results indicate that MLR model forecast are closely matching with actual observations values, artificial neural network model over-forecast some days volume of daily water supply by FCTWB, cooperation and multiple nonlinear regression model under-forecast some days volume of daily water supply by FCTWB, corporation. The three models compared depicts the influential variables of FCTWB Corporation daily water supply, (ANN = DWP, DWT), (MLR = DWT, DWL) and (MNLR = DWP, DWL), and their forecast graphs shows downward daily water supply in FCT, Abuja. It is recommended that the FCT, Abuja water Board Corporation should consider multiple linear regression (MLR) model and its forecasted values as a road map in its operations and planning toward water supply sustainability in FCT, Abuja.

Investigation of river flow volume in different conditions as a function of temperature and rainfall variables can be quite effective in understanding the hydrological and hydro-climatic conditions of the watershed. Multiple linear regression models were applied in estimating river flow in several studies due to their straightforwardness and appropriate interpretation of results. In this study, to overcome the limitations of the multiple linear regression model, the Bayesian quantile regression model was used to estimate the river flow volume as a function of rainfall and temperature, and the results were compared. The data and information used for the Qareh-Sou basin in northern Iran are of substantial environmental and socio-economic importance. Five data series, including spring, summer, autumn, winter, and annual series, were created and used for this study. It was found that the Bayesian quantile regression model has considerable flexibility to model the volume of flow for different quantiles, predominantly upper and lower quantiles, and can be used to model high and low flows. With increasing the values of quantiles, a limited decreasing pattern in the effect of rainfall on the volume of flow was identified, which can be due to increasing the effect of other factors in the formation of extreme flows of the river. For summer data in high quantiles, the effect of rainfall on river flow volume shows an increasing pattern. This pattern is different from the other studied series, which may be due to the low base flow in summer. The results confirm that the application of Bayesian quantile regression compared to multiple linear regression leads to much more valuable information on the impact of rainfall and temperature on river flow volume.

Estimating olive (Olea europaea L.) leaf area is an important aspect of monitoring plant health and evaluating growth processes in agriculture. Accurate estimation of leaf area allows for a better understanding of processes such as water and nutrient utilization, photosynthesis efficiency, respiration, and yield potential. This study aims to determine the most accurate, easy, and reliable leaf area estimation model using the geometric properties (length and width) of olive leaves. Additionally, the predictive performances of multiple linear regression (MLR) and artificial neural network (ANN) were compared. A total of 1320 leaf samples collected from 22 olive cultivars were used in the study. Leaf length and width were taken as input parameters, and both MLR and ANN models were developed for each cultivar. Both multiple linear regression (MLR) and artificial neural network (ANN) models demonstrated high predictive accuracy for olive leaf area estimation across 22 cultivars. The MLR models explained up to 96% of the variation in leaf area using leaf length (LL) and leaf width (LW), with low root mean square errors, indicating strong reliability. When cultivar identity was modeled as a categorical factor through dummy encoding, the model captured significant cultivar-specific effects without altering the overall predictive performance. The ANN models achieved slightly higher accuracy, with determination coefficients exceeding 0.99 and minimal prediction errors, confirming their superior ability to model nonlinear relationships. Across both approaches, leaf width contributed more strongly to leaf area than leaf length. Cultivar-specific differences were statistically significant for only a few genotypes, while most cultivars exhibited comparable patterns after adjustment for multiple testing. In conclusion, both MLR and ANN models demonstrated high accuracy in predicting olive leaf area, with ANN models showing slightly superior performance. However, MLR models also yielded highly reliable results, indicating that both approaches are viable for practical applications in olive cultivation. These predictive models can be effectively used for rapid, non-destructive phenotyping, growth monitoring, and precision management in olive breeding and production systems.

با برآورد ظرفیت تبادل کاتیونی با استفاده از ویژگی‏های پایه ای و زودیافت خاک می‏توان در وقت و هزینه صرفه‏جویی کرد. هدف این بررسی، مقایسه دو روش رگرسیون درختی و رگرسیون خطی چندگانه در برآورد ظرفیت تبادل کاتیونی (CEC) با استفاده از ویژگی‏هایخاک است. برای این منظور از داده های 106 نمونه خاک UNSODA استفاده شد. جهت برآورد CEC با استفاده از روش‏های رگرسیون درختی و رگرسیون خطی از ویژگی های اجزای بافت خاک،pH، ماده آلی و چگالی ظاهری استفاده شد. کارآیی روش رگرسیون درختی در برابر روش رگرسیون خطی چندگانه در برآورد CEC مقایسه شدند. نتایج نشان داد که در برآورد CEC با استفاده از روش های رگرسیونی تنها ضرایب ماده آلی (183/3) و درصد رس (274/0) که بیشترین همبستگی را با CEC دارند معنی دار شده و مدل رگرسیونی بر اساس این دو پارامتر توسعه یافت. همچنین از میان پارمترهای ورودی در روش رگرسیون درختی تنها پارامترهای ماده آلی و درصد رس در درخت رگرسیون ظاهر شد. روش رگرسیون درختی در دو مجموعه داده صحت سنجی و اعتبار سنجی بر اساس آماره های ارزیابی R2، RMSE، ME و GMER کارآیی بالاتری نسبت به روش های رگرسیونی خطی در برآورد CEC داشت. از میان روش های رگرسیونی خطی، مدل پیشنهادی کارآیی بالاتری نسبت به مدل های بل و ونکولن و بروسما و همکاران داشت.

Purpose – This paper aims to predict the needle penetration force (NPF) in denim fabrics using the artificial neural network (ANN) and multiple linear regression (MLR) models based on the effects of various sewing parameters. Design/methodology/approach – In order to design the ANN and MLR models, four parameters including fabric weight, number of fabric layers, weave pattern, and sewing needle size are taken into account as the input parameters and NPF as the output parameter. According to these parameters, 140 samples of data were resulted. Each sample was tested five times. From these 140 data (input-output data pairs), 112 were used for training the ANN and MLR models and 28 samples were used to test the performance of ANN and MLR. Also, the NPF was measured on the Instron tensile tester to simulate sewing process. Findings – The results indicated that the NPF in denim fabrics can be well predicted in terms of sewing parameters by using ANN and MLR models, in which the ANN model exhibits greater performance than MLR (RANN=0.989> RMLR=0.901). Research limitations/implications – The NPF measurement method is limited at low speed. Originality/value – Using the ANN model for forecasting NPF in denim fabrics can help the garment manufactures to produce high-quality denim products and improve the sewing process through reducing seam damage. The NPF could be also measured in the cycle loading conditions similar to sewing machine process by using a special designed tools mounted on the Instron tensile tester.

The purpose of our study was the evaluation of the most important factors that affect the volumetric and conventional mechanical properties of produced asphalt mix and the volumetric properties of built‐in asphalt layer. Asphalt mix design follows the standard procedure (Marshall procedure). We were interested not only in the quantity of bitumen specified by the Marshall procedure, but also in the quantity of stone aggregate fractions, temperatures of production and properties of bitumen that is used. The influence of these factors was investigated with several models. For the building of models we used 444 asphalt samples, analysed by one laboratory. To select the most important factors, several multiple linear regression (MLR) models, partial least squares (PLS) regression models and counterpropagation neural network models were made. Obtained models were tested with leave‐one‐out (LOO) and leave‐10%‐out cross‐validation procedures. The results of MLR and PLS models show that the independent variables are closely related. Among 21 variables there is only one found as less important. MLR and PLS models show better predictive ability than counterpropagation neural network models. The best MLR models will be employed for the preparation of the asphalt mix design (recipe) with some unknown material. Copyright © 2009 John Wiley & Sons, Ltd.

Estimating wet soil aggregate stability from easily available properties in a highly mountainous watershed

Evaluation and prediction of shrub cover in coastal Oregon forests (USA)

Childhood and adolescent overweight and obesity are one of the most serious public health challenges of the 21st century. A range of genetic, family, and environmental factors, and health behaviors are associated with childhood obesity. Developing models to predict childhood obesity requires careful examination of how these factors contribute to the emergence of childhood obesity. This paper has employed Multiple Linear Regression (MLR), Random Forest (RF), Decision Tree (DT), and K-Nearest Neighbour (KNN) models to predict the age at the onset of childhood obesity in Saudi Arabia (S.A.) and to identify the significant factors associated with it. De-identified data from Arar and Riyadh regions of S.A. were used to develop the prediction models and to compare their performance using multi-prediction accuracy measures. The average age at the onset of obesity is 10.8 years with no significant difference between boys and girls. The most common age group for onset is (5-15) years. RF model with the R2 = 0.98, the root mean square error = 0.44, and mean absolute error = 0.28 outperformed other models followed by MLR, DT, and KNN. The age at the onset of obesity was linked to several demographic, medical, and lifestyle factors including height and weight, parents’ education level and income, consanguineous marriage, family history, autism, gestational age, nutrition in the first 6 months, birth weight, sleep hours, and lack of physical activities. The results can assist in reducing the childhood obesity epidemic in Saudi Arabia by identifying and managing high-risk individuals and providing better preventive care. Furthermore, the study findings can assist in predicting and preventing childhood obesity in other populations.

The objective of the research work was to estimate the economic valuation for the conservation and/or protection of the Las Orquideas to Naranjillo section of the Huallaga River on behalf of the population in Tingo Maria, [Peru], and the nearby areas. In order to estimate the willingness to pay (WTP; DAP in Spanish), a survey was done [with a] questionnaire, organized according to the contingent valuation method. For the statistical analysis, the probabilistic, logistic, and multiple linear regression econometric models were used. According to the results of the analysis, it was concluded that the demand curve of the probabilistic model was: WTP-P = 1.097*X7 + 0.762*X12 + 0.443*X13 – 0.219*X16 – 0.582*X17; [for the] logistic model, it was: WTP-L = 1.811*X7 + 1.313*X12 + 0.778*X13 – 0.374*X16 – 0.999*X17; and [for the] multiple linear regression model, it was: WTP-RLM = 0.494 + 0.051*X1 + 0.267*X7 + 0.194*X12 + 0.109*X13 – 0.062*X16 – 0.169*X17; where X1: type of home, X7: assessment of the Huallaga River, X12: intervention [in the] conservation of the Huallaga River, X13: level of education, X16: price they were willing to pay, and the WTP. The average willingness to pay predicted at 84.54% [accuracy]. For the probabilistic model, the average WTP was 6.87 soles, with a variation of 52.97%; [for] the logistic model, the average WTP was 6.84 soles, with a variation of 52.60%; and [for] the multiple linear regression model, the average WTP was 14.92 soles, with a variation of 23.10%.

Pseudomonas chlororaphis 3732RN-L11 survival rates in soil and wheat rhizosphere were measured using intact soil core microcosms representing 23 sites across Canada. Linear multiple regression (LMR) models were developed to predict the survival rate of this genetically engineered microorganism (GEM) as a function of soil parameters measured at the time of microcosm inoculation. LMR models were tested by comparing their predicted survival rates with observed survival rates from environmental introductions of the GEM by Gagliardi et al. (2001) at five field sites across Canada over two years. No soil parameter (e.g., % clay) was highly correlated with GEM survival rates in soil or wheat rhizosphere. Total fungal colony-forming units (CFUs), % soil titanium (positive correlations), and % soil magnesium (negative correlation) were found to be the best LMR predictors of GEM survival rates in soil over two years. Total soil bacterial CFUs, nitrate, % soil potassium (positive correlations), and exchangeable magnesium (negative correlation) were found to be the best LMR predictors of GEM survival rate in wheat rhizosphere over two years. While LMR models were statistically significant, they were unable to reliably predict the survival rate of the GEM in field trial introductions. The results indicate that there can be considerable uncertainty associated with predicting GEM survival for multi-site environmental introductions.

Response factors were determined for twelve GXG peptides (where G stands for glycine and X is any of alanine [A], arginine [R], asparagine [N], aspartic acid [D], glycine [G], histidine [H], leucine [L], lysine [K], phenylalanine [F], serine [S], tyrosine [Y], valine [V]) by electrospray ionization mass spectrometry (ESI-MS). The response factors were measured using a novel flow injection method. This new method is based on the Gaussian distribution of analyte concentration resulting from band-broadening dispersion experienced by the analyte upon passage through an extended volume of PEEK tubing. This method removes the need for preparing a discrete series of standard solutions to assess concentration-dependent response. Relative response factors were calculated for each peptide with reference to GGG. The observed trends in the relative response factors were correlated with several analyte physicochemical parameters, chosen based on current understanding of ion release from charged droplets during the ESI process. These include analyte properties: nonpolar surface area; polar surface area; gas-phase basicity; proton affinity; and Log D. Multivariate statistical analysis using multiple linear regression, decision tree, and support vector regression models were investigated to assess their potential for predicting ESI response based on the analyte properties. The support vector regression model was more versatile and produced the least predictive error following 12-fold cross-validation. The effect of variation in solution pH on the relative response factors is highlighted, as evidenced by the different predictive models obtained for peptide response at two pH values (pH = 6.0 and 9.0). The relationship between physicochemical parameters and associated ionization efficiencies for GXG tripeptides is discussed based on the equilibrium partitioning model.

The service sector remains the only economic sector that has recorded an increase (3.8%) in energy consumption during the last decade, and it is projected to grow more than 50% in the following decades. Among the public buildings, educational are especially important since they have high abundance, great retrofit potential in terms of energy savings and impact in promoting a culture of energy efficiency. Since predictive models have shown high potential in optimizing usage of energy in buildings, this study aimed to assess their application for both finding the most influential factors on heat consumption in public kindergarten and heat consumption prediction. Two linear (simple and multiple linear regression) and two non-linear (decision tree and artificial neural network) predictive models were utilized to estimate monthly heat consumption in 11 public kindergartens in the city of Kragujevac, Serbia. Top-performing and most complex to develop was the artificial neural network predictive model. Contrary to that, simple linear regression was the least precise but the most simple to develop. It was found that multiple linear regression and decision tree were relatively simple to develop and interpret, where in particular the multiple linear regression provided relatively satisfying results with a good balance of precision and usability. It was concluded that the selection of proper predictive methods depends on data availability, and technical abilities of those who utilize and create them, often offering the choice between simplicity and precision.

ABSTRACTThe current study aims to predict the thermal runaway in lithium‐ion batteries using five artificial intelligence algorithms, considering the environmental factors and various design parameters. Multiple linear regression, k‐nearest neighbors, decision tree, and random forest are used as machine learning algorithms, while artificial neural networks are used as deep learning algorithms. Nineteen experimental datasets are used to train the models. First, Pearson's correlation matrix is used to investigate the effects of input parameters on the thermal runaway onset time. The dataset is then updated to include only tests with thermal runaway produced by an external heat source. As a result of comparison among model performance prediction, it is determined that the decision tree model is the best‐performing model with a coefficient of determination (R2) score of 0.9881, followed by random forest, k‐nearest neighbors, artificial neural networks, and multiple linear regression models. The dataset is modified when the thermal runaway is triggered by external heating and compression forces. Results show that in this case, the performance of the decision tree model has an R2 of 0.9742. Finally, the force range in which the model has the best performance is predicted, which is helpful in conducting tests to obtain reliable results.

Revisiting useful approaches to data-rich macroeconomic forecasting