Towards an Error Correction Model for dam monitoring data analysis based on Cointegration Theory

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.

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.

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

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.

This paper is focusing on the application of robust method in multiple linear regression (MLR) model towards diabetes data. The objectives of this study are to identify the significant variables that affect diabetes by using MLR model and using MLR model with robust method, and to measure the performance of MLR model with/without robust method. Robust method is used in order to overcome the outlier problem of the data. There are three robust methods used in this study which are least quartile difference (LQD), median absolute deviation (MAD) and least-trimmed squares (LTS) estimator. The result shows that multiple linear regression with application of LTS estimator is the best model since it has the lowest value of mean square error (MSE) and mean absolute error (MAE). In conclusion, plasma glucose concentration in an oral glucose tolerance test is positively affected by body mass index, diastolic blood pressure, triceps skin fold thickness, diabetes pedigree function, age and yes/no for diabetes according to WHO criteria while negatively affected by the number of pregnancies. This finding can be used as a guideline for medical doctors as an early prevention of stage 2 of diabetes.

Multiple linear regression (MLR) models for fast estimation of true subsurface resistivity from apparent resistivity field measurements are developed and assessed in this study, based on Dipole-dipole array. The parameters that have been investigated are apparent resistivity (ρa) horizontal location (X) and depth (Z) of measurement as the independent variables; and true resistivity (ρt) as dependent variable. To achieve linearity in both resistivities, datasets were first transformed into logarithmic domain following diagnostic checks of normality of the dependent variable and heteroscedasticity to ensure accurate models. Four MLR models namely; DD1, DD2, DD3 and DD4 were developed based on hierarchical combination of the independent variables. The generated MLR coefficients were applied to another dataset to estimate ρt values for validation. The accuracy of the models was assessed using coefficient of determination (R2), standard error (SE) and weighted mean absolute percentage error (wMAPE). It is concluded that the MLR models can estimate ρt for the Dipole-dipole array with high level of accuracy, with the DD4 model being the best.

Comparative study of multiple linear regression (MLR) and artificial neural network (ANN) techniques to model a solid desiccant wheel

The performance of Autoregressive Moving Average and Multiple Linear Regression Models in predicting minimum and maximum temperatures of Ogun State is herein reported. Maximum and Minimum temperatures data covering a period of 29 years (1982 -2009) obtained from the Nigerian Meteorological Agency (NiMet), Abeokuta office, Nigeria, were used for the analyses. The data were first processed and aggregated into annual time series. Mann-Kendal non-parametric test and spectral analysis were carried out to detect whether there is trend, seasonal pattern, and either short or long memory in the time series. Mann-Kendal Z-values obtained are –0.47 and –2.03 for minimum and maximum temperatures respectively, indicating no trend, though the plot shows a slight change. The Lo’s R/S Q(N,q) values for minimum and maximum temperatures are 3.67 and 4.43, which are not within the range 0.809 and 1.862, thus signifying presence of long memory. The data was divided into two and the first 20 years data was used for model development, while the remaining was used for validation. Autoregressive Moving Average (ARMA) model of order (5, 3) and Autoregressive (AR) model of order 2 are found best for predicting minimum and maximum temperatures respectively. Multiple Linear Regression (MLR) model with 4 features (moving average, exponential moving average, rate of change and oscillator) were fitted for both temperatures. The ARMA and AR models were found to perform better with Mean Absolute Percentage Error (MAPE) values of -2.89 and -1.37 for minimum and maximum temperatures, compared with the Multiple Linear Regression Models with MAPE values of 141 and 876 respectively. Results of ARMA model can be relied on in generating forecast of temperature of the study area because of their minimal error values. However, it is recommended other climatic elements that were not captured in this paper due to unavailability of information be considered too in order to see which model is best for them.

Western Disturbances (WDs) are the primary contributor of winter precipitation over the Western Himalayas (WH). The precipitation falling as snow is essential for Himalayan glaciers accumulation, contributing to Himalayan rivers supporting downstream population of the Indian subcontinent. Climate change has affected the Himalayas, which is noticeable through lesser snowfall and higher melt leading to critical water resource stresses and managements. Available climate models are one of the best available tools to assess precipitation changes over and around the Himalayas. Inherent uncertainties and errors in these numerical models need a certain urge for improvement. Integration of statistical models and methods on top of dynamical models provide better insight and utility in associated processes. Thus, a statistical relationship between various predictors and precipitation over the region is investigated. Available observations from APHRODITE and ERA‐I and model fields from EC‐EARTH‐RCA4 (a CORDEX‐SA member) is used. Multiple linear regression (MLR) model is used to establish statistical estimates using meteorological variables as predictors and precipitation. The correlation between the predictors and precipitation is determined, and a contour depicting maximum correlation is used to estimate regression coefficients. The MLR model is trained during present (1987–2005) and tested during 2006–2007. Higher positive correlations between observations and MLR model are found. This developed MLR model is then implemented for assessing future WDs under RCP8.5 scenario. The intensity and frequency of WDs are calculated during the present and future. Model‐based WDs' intensities slightly deviate from the corresponding observations in present. But the model‐based WDs' frequencies match with the corresponding observations in present. The results indicate that WDs show a decreasing trend in frequency and intensity in the present and near‐future. But in far‐future intensity of WDs shows an increasing trend.

The applicability of artificial neural networks (ANNs) and the adaptive neuro-fuzzy inference system (ANFIS) for determination of mean velocity and discharge of natural streams is investigated. The 2,184 field data obtained from four different sites on the Sarimsakli and Sosun streams in central Turkey were used in the study. ANNs and ANFIS models use the inputs, water surface velocity and water surface slope, to estimate the mean velocity and discharges of natural streams. The accuracies of both models were compared with the multiple-linear regression (MLR) model. The comparison results showed that the ANFIS model performed better than the ANNs and regression models for estimating mean velocity and discharge. The ANN model also showed better accuracy than the MLR model. The root mean square errors (RMSE) and mean absolute relative errors (MARE) of the MLR model were reduced by 88 and 91 % using the ANFIS model in estimating discharges, respectively. It is found that the optimal ANFIS model with RMSE of 0,063, MARE of 3,47 and determination coefficient (R2) of 0,996 in the test period is superior in estimation of discharge than the MLR model with RMSE of 0,532, MARE of 38,9 and R2 of 0,776, respectively. The study reveals that the ANFIS technique can be successfully used for estimating the mean velocity and discharge of natural streams by using only the inputs of water surface velocity and water surface slope.

This study presents a meta-analysis of 12 experiments that quantify nitrate-N leaching losses from grazed pasture systems in alluvial sedimentary soils in Canterbury (New Zealand). Mean measured nitrate-N leached (kg N/ha × 100 mm drainage) losses were 2.7 when no urine was applied, 8.4 at the urine rate of 300 kg N/ha, 9.8 at 500 kg N/ha, 24.5 at 700 kg N/ha and 51.4 at 1000 kg N/ha. Lismore soils presented significantly higher nitrate-N losses compared to Templeton soils. Moreover, a multiple linear regression (MLR) model was developed to determine the key factors that influence nitrate-N leaching and to predict nitrate-N leaching losses. The MLR analyses was calibrated and validated using 82 average values of nitrate-N leached and 48 explanatory variables representative of nitrogen inputs and outputs, transport, attenuation of nitrogen and farm management practices. The MLR model (R (2) = 0.81) showed that nitrate-N leaching losses were greater at higher urine application rates and when there was more drainage from rainfall and irrigation. On the other hand, nitrate leaching decreased when nitrification inhibitors (e.g. dicyandiamide (DCD)) were applied. Predicted nitrate-N leaching losses at the paddock scale were calculated using the MLR equation, and they varied largely depending on the urine application rate and urine patch coverage.

To non-destructively and rapidly monitor the chlorophyll content of winter wheat leaves under CO2 microleakage stress, and to establish the quantitative relationship between chlorophyll content and sensitive bands in the winter wheat growing season from 2023 to 2024, the leakage rate was set to 1 L/min, 3 L/min, 5 L/min, and 0 L/min through field experiments. The dimensional reduction was realized, fractional differential processing of a wheat canopy spectrum was carried out, a multiple linear regression (MLR) and partial least squares regression (PLSR) estimation model was constructed using a SPA selection band, and the model's accuracy was evaluated. The optimal model for hyperspectral estimation of wheat SPAD under CO2 microleakage stress was screened. The results show that the spectral curves of winter wheat leaves under CO2 microleakage stress showed a "red shift" of the green peak and a "blue shift" of the red edge. Compared with 1 L/min and 3 L/min, wheat leaves were more affected by CO2 at 5 L/min. Evaluation of the accuracy of the MLR and PLSR models shows that the MLR model is better, where the MLR estimation model based on 1.1, 1.8, 0.4, and 1.7 differential SPAD is the best for leakage rates of 1 L/min, 3 L/min, 5 L/min, and 0 L/min, with validation set R2 of 0.832, 0.760, 0.928, and 0.773, which are 11.528, 14.2, 17.048, and 37.3% higher than the raw spectra, respectively. This method can be used to estimate the chlorophyll content of winter wheat leaves under CO2 trace-leakage stress and to dynamically monitor CO2 trace-leakage stress in crops.

In this study, artificial neural networks (ANNs) were employed to investigate the relationship between locomotion score and production traits. A total number of 123 dairy cows from a free-stall housing farm were used in this study. To compare the effectiveness of the ANNs for the prediction of locomotion score, the multiple linear regression (MLR) model was developed using the eight production traits, body condition score, parity, days in milk, daily milk yield, milk fat percent, milk protein percent, daily milk fat yield, and daily milk protein yield as input variables to predict the locomotion score. The ANN predictions gave a higher coefficient of determination (R2) values with lower mean squared error (MSE) than MLR. The R2 and MSE of the MLR model were 0.53 and 0.36, respectively. However, the ANN model for the same dataset produced much improved results with R2 = 0.80 ‏ and MSE = 0.16, respectively. Globally, the results of this study showed that the connectionist network model was a better tool to predict locomotion scores compared to the multiple linear regression.