Robust Method in Multiple Linear Regression Model on Diabetes Patients

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.

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.

Full text Figures and data Side by side Abstract Editor's evaluation Introduction Materials and methods Results Discussion Data availability References Decision letter Author response Article and author information Metrics Abstract Background: Oxygen uptake (VO2) is one of the most important measures of fitness and critical vital sign. Cardiopulmonary exercise testing (CPET) is a valuable method of assessing fitness in sport and clinical settings. There is a lack of large studies on athletic populations to predict VO2max using somatic or submaximal CPET variables. Thus, this study aimed to: (1) derive prediction models for maximal VO2 (VO2max) based on submaximal exercise variables at anaerobic threshold (AT) or respiratory compensation point (RCP) or only somatic and (2) internally validate provided equations. Methods: Four thousand four hundred twenty-four male endurance athletes (EA) underwent maximal symptom-limited CPET on a treadmill (n=3330) or cycle ergometer (n=1094). The cohort was randomly divided between: variables selection (nrunners = 1998; ncyclist = 656), model building (nrunners = 666; ncyclist = 219), and validation (nrunners = 666; ncyclist = 219). Random forest was used to select the most significant variables. Models were derived and internally validated with multiple linear regression. Results: Runners were 36.24±8.45 years; BMI = 23.94 ± 2.43 kg·m−2; VO2max=53.81±6.67 mL·min−1·kg−1. Cyclists were 37.33±9.13 years; BMI = 24.34 ± 2.63 kg·m−2; VO2max=51.74±7.99 mL·min−1·kg−1. VO2 at AT and RCP were the most contributing variables to exercise equations. Body mass and body fat had the highest impact on the somatic equation. Model performance for VO2max based on variables at AT was R2=0.81, at RCP was R2=0.91, at AT and RCP was R2=0.91 and for somatic-only was R2=0.43. Conclusions: Derived prediction models were highly accurate and fairly replicable. Formulae allow for precise estimation of VO2max based on submaximal exercise performance or somatic variables. Presented models are applicable for sport and clinical settling. They are a valuable supplementary method for fitness practitioners to adjust individualised training recommendations. Funding: No external funding was received for this work. Editor's evaluation The authors have established new formulas to predict maximum oxygen uptake for cyclists and runners based on submaximal exercise testing and anthropometric characteristics. This is an important study with a large and comprehensive dataset, which may be helpful for many exercise labs. The work is convincing, using appropriate and validated methodology in line with the current state-of-the-art, as shown by references to common exercise books. https://doi.org/10.7554/eLife.86291.sa0 Decision letter Reviews on Sciety eLife's review process Introduction The oxygen uptake (VO2) is considered an important metric in assessing cardiorespiratory fitness, health status, or endurance performance potential (Guazzi et al., 2012). With the application of standardised procedures and interpretation protocols, during graded exercise tests (GXT), the (maximal oxygen uptake) VO2max can be established (Bentley et al., 2007). GXT is the most widely used assessment to examine the dynamic relationship between exercise and integrated physiological systems (Albouaini et al., 2007; Bentley et al., 2007). The information from GXT during cardiopulmonary exercise testing (CPET) can be applied across the spectrum of sport performance, occupational safety screening, research, and clinical diagnostics (Guazzi et al., 2017). VO2 max is often used as a boundary between severe and extreme intensity domains and by definition requires maximal effort from the tested subject (Gaesser and Poole, 1996). However, it is not always recommended or possible to undertake a test to exhaustion (Guazzi et al., 2012). For the athletes, the proximity of competition or injury history can allow submaximal testing, but not testing to exhaustion (Sassi et al., 2006). Testing that requires maximal effort may be disruptive to the training process or interfere with race performance (Coutts et al., 2007; Lamberts et al., 2011). Due to practical constraints, tests to exhaustion or peak-power-output tests are often performed only two or three times a year (Coutts et al., 2007). However, VO2 values are widely used in sport science and the decision-making process (Mann et al., 2013). VO2 is widely considered one of the major endurance performance determinants (Joyner and Coyle, 2008). Using VO2max to guide the selection process, prescribing training intensity, assessing training adaptations, or predicting race times is a common practice in high-performance sports (Bassett and Howley, 2000; Bentley et al., 2007; Hawley and Noakes, 1992; Noakes et al., 1990). VO2max is also one of the critical vital signs coordinating the function of the cardiovascular, respiratory, and muscular systems, it is an indicator of overall body health status (Kaminsky et al., 2017). Quantifying VO2max provides additional input regarding clinical decision-making, risk stratification, evaluation of therapy, and physical activity guidelines (Guazzi et al., 2012). For patients undertaking a test to exhaustion is rarely needed or possible due to health restraints or cardiac risk (Guazzi et al., 2016). For many years researchers have studied indirect methods of estimating VO2max(Sartor et al., 2013). Protocols such as the Astrand-Ryhming Test, Six-Minute Walk Test, or YMCA Step Test have been established and validated (Astrand and Ryhming, 1954; Beutner et al., 2015; Carey, 2022; Jalili et al., 2018). Moreover, estimation of the VO2 and heart rate (HR) values below the ventilatory threshold can be based on cardiorespiratory kinetics assessment using randomised changes in the work rate known as a pseudo-random binary sequences testing (Hoffmann et al., 2022). However, with the development of technology, the accessibility of laboratory testing and mobile testing improved (Montoye et al., 2020; Pritchard et al., 2021). Therefore, new opportunities to develop more precise yet simple and accessible methods and models to assess VO2max occur (Jurov et al., 2023). This appears to be especially important considering the low prediction accuracy of most of the VO2max formulae that were validated in our previous study (Wiecha et al., 2023). Recently, we have been observing the development of prediction methods with the usage of machine learning (ML) and artificial intelligence (AI) (Ashfaq et al., 2022). Both ML and AI are used in sport science as forecasting and decision-making support tools (Abut and Akay, 2015; Bobowik and Wiszomirska, 2022; Chmait and Westerbeek, 2021; Hammes et al., 2022; Rossi et al., 2021). There is growing evidence that VO2max prediction based on ML models, especially support vector ML and artificial neural network models, exhibits more robust and accurate results compared to MLR only (Abut and Akay, 2015; Ashfaq et al., 2022). Therefore, in this research, with the support of ML, we look for algorithms and prediction patterns that allow us to use values obtained during submaximal CPET and somatic measurements to estimate maximal VO2max values in male runners and cyclists. We stipulate that prediction models allow for accurate calculation of VO2max based on somatic or submaximal CPET variables. Materials and methods We have applied the development and validation of the prediction TRIPOD guidelines to conduct the study (see Supplementary Material 1TRIPOD Checklist for Prediction Model Development and Validation) (Collins et al., 2015). The study is based on retrospective data analysis from the CPET registry collected from 2013 to 2021 at the medical clinic (Sportslab, Warsaw, Poland). All CPET have been performed at the individual request of participants, as a part of regular training monitoring or performance assessment. Ethical approval Request a detailed protocol The Institutional Review Board of the Bioethical Committee at the Medical University of Warsaw (AKBE/32/2021) has approved the study protocol. The regulations of the Declaration of Helsinki were met during all parts of the study. Each study participant delivered written consent to undergo CPET and participate in the study. Derivation cohort Request a detailed protocol We selected the cohort with the use of rigorous exclusion/inclusion criteria. Due to the insufficient number of women in our database and the number of potential variables in the regression models for adequate power, we had to limit ourselves to conduct analysis in the male population only (Martens and Logan, 2021). Out of 6439 healthy, adult male cyclists and long-distance runners that undergone CPET, 4423 met the criteria as further: (1) age ≥18 years, (2) declared regular cycling or running training for ≥3 months, (3) had no extreme outliers ≤ or ≥±3 standard deviations (SD) from mean for all of the testing variables (beyond ≥±3 SD in VO2max), (4) lack of any injury, medical condition, or addiction in medical history that may affect exercise capacity, (5) not taking any medications with a modifying effect on exercise capacity, (6) maximum exertion achieved during CPET. We defined the maximum exertion in CPET as the fulfilment of the minimum six of the following criteria: (1) respiratory exchange ratio (RER) ≥1.10, (2) present VO2 plateau (growth <100 mL·min–1 in VO2 despite increased running speed or cycling power), (3) respiratory frequency (fR) ≥45 breaths·min–1, (4) declared subjective exertion intensity during CPET ≥18 in the Borg scale (Borg, 1970), (5) blood lactate concentration [La-]b ≥8 mmol·L–1, (6) growth in speed/power ≥10% of respiratory compensation point (RCP) values after exceeding the RCP, (7) peak heart rate (HRpeak) ≥15 beats·min–1 below predicted maximal heart rate (HRmax) (Lach et al., 2021). Participants’ selection procedure has been shown in Figure 1. Figure 1 Download asset Open asset Flowchart of the preliminary inclusion and exclusion process. Abbreviations: EA, endurance athlete; CPET, cardiopulmonary exercise testing; SD, standard deviation; TE, treadmill; RER, respiratory exchange ratio; VO2, oxygen uptake (mL·min−1·kg−1); [La−]b, lactate concentration (mmol·L−1); fR, breathing frequency (breaths·min−1); RCP, respiratory compensation point; HRpeak, peak heart rate (beats·min−1); HRmax, maximal heart rate (bpm). At both stages of the selection, some participants met several (>1) exclusion criteria. Somatic measurements and CPET protocols Request a detailed protocol Body mass was measured with a body composition (BC) analyser (Tanita, MC 718, Japan) with the multifrequency of 5 kHz/50 kHz/250 kHz via the bioimpedance analysis and normal testing mode. The participants’ skin was cleaned with alcohol before placing the electrodes on the skin. Prior to the test, the participants received instructions to refrain from exercising for 2 hr, consume a light meal rich in carbohydrates 2–3 hr beforehand, and maintain hydration by drinking isotonic beverages. Additionally, they were advised to abstain from medications, caffeine, and cigarettes on the day of the test. Running CPET (TE) was performed on a mechanical treadmill (h/p/Cosmos Quasar, Germany). Cycling CPET (CE) was performed on Cyclus-2 (RBM elektronik-automation GmbH, Leipzig, Germany). Hans Rudolph V2 mask (Hans Rudolph, Inc, Shawnee, KS, USA), breath-by-breath method with Cosmed Quark CPET gas exchange analysing device (Cosmed Srl, Rome, Italy), and Quark PFT Suite to Omnia 1.6 software were utilised. The gas analyser device was regularly calibrated with the reference gas (16% O2; 5% CO2) in accordance with the manufacturer’s instructions (Airgas USA, LLC, Plumsteadville, PA, USA). From 2013 to 2021, three Cosmed Quark CPET units were used. HR was measured with the Cosmed torso belt (Cosmed srl, Rome, Italy). [La-]b was measured via enzymatic-amperometric electrochemical technique with Super GL2 analyser (Müller Gerätebau GmbH, Freital, Germany). The [La-]b analyser was regularly calibrated before each measurement series. The 40 m2 indoor, air-conditioned laboratory with 20–22°C temperature and 40–60% humidity, and 100 m ASL provided the same conditions for all BC and CPET. Each CPET began with a 5 min personalised warm-up (walk or easy jog with ‘conversational’ intensity for running, easy pedalling with ‘conversational’ intensity for cycling). Then after the preparation (about 5 min), the continuous progressive step test was conducted. Due to the population diversity (training status), the running test speed started from 7 to 12 km·hr–1 with a 1% treadmill incline. The choice of initial starting speed was determined by the interview and sports results achieved. For example, those running less than 60 min at a distance of 10 km started the test at 7 km/hr, while those running 10 km for less than 35 min started the test at an initial speed of 12 km/hr. The pace increased by 1 km·hr–1 every 2 min with no change in incline. The cycling test began at 60–150 W, depending on the athletes training status. The power increased by 20–30 W every 2 min. It was recommended to maintain a constant cadence of 80–90 (repetition·min–1) during the test. The tests were terminated due to exhaustion: volitional inability to continue the activity or/and VO2 and HR plateau with increasing load or/and observed disturbance of coordination in running or/and inability to maintain the set cadence. Due to the graded protocol used, the cycling power and running speed values have been calculated as a function of time to better reflect the actual level for the test moment being determined (Kuipers et al., 1985). Before the test, after every step, and 3 min after the termination of the effort technician took a 20 µL blood sample from a fingertip. Samples were collected during the test without interrupting the effort. The samples were taken from the initial puncture. The first blood drop was collected into the swab and the second blood drop was drawn for further analysis into the capillary. VO2max was recorded as the highest value (15 s intervals) before the termination of the test. HRmax was recorded as the highest value obtained at the end of the test, without averaging. The anaerobic threshold (AT) was established with the following criteria: (1) common start of VE/VO2 and VE/VCO2 curves, (2) end-tidal partial pressure of oxygen raised constantly with the end-tidal partial pressure of carbon dioxide (Beaver et al., 1986). The was established with the following criteria: (1) PetCO2 must decrease after reaching maximal amount, (2) the presence of fast nonlinear growth in VE (second deflection), (3) the VE/VCO2 ratio achieved minimum and started to rise, and (4) a nonlinear increase in VCO2 versus VO2 (lack of linearity) (Beaver et al., 1986). The [La-]b was estimated for AT and RCP in relation to power or speed (Wiecha et al., 2022). Data analysis Request a detailed protocol Our comprehensive ML approach enables the evaluation of each formula by preliminary variables precision (at the stage of selection), then accuracy (during the model’s building) and recall (in internal validation). Individual CPET results were saved into the Excel file (Microsoft Corporation, Redmond, WA, USA) and a custom-made script was used to generate the database in Excel (Python programming). Further, mean, SD, and 95% confidence intervals (CI) were calculated. The normality of the distribution of the data was examined using the Shapiro-Wilk test and intergroup differences were calculated using the Student’s t-test for independent variables. Three-step variable selection procedures based on random forests were applied using the R package VSURF in RStudio software (R Core Team, Vienna, Austria; version 3.6.4) (Genuer et al., 2016). For each level of measurement (AT, RCP) and their combination (AT+RCP), significant variables were identified separately. The first step was dedicated to eliminate irrelevant variables from the dataset. Second step aimed to select all variables related to the response for interpretation purposes. The third step refined the selection by eliminating redundancy in the set of variables selected by the second step, for prediction purposes (Genuer et al., 2017). Each time for variables selection, the anthropometric variables as in Tables 1–2 and the CPET parameters given in Tables 3–4 from a specific level of measurement (AT; RCP) and their combinations were visible. Table 1 Basic anthropometric characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDAge (years)36.235.6–36.98.4535.935.5–36.38.0535.534.9–36.28.14Height (cm)180.0179.6–180.56.04179.4179.1–179.76.13179.7179.2–180.26.61BM (kg)77.777.0–78.49.3577.777.3–78.19.2977.977.1–78.610.1BMI (kg·m–2)23.923.8–24.12.4324.124.0–24.22.4124.123.9–24.32.56BF (%)15.415.1–15.74.5515.515.3–15.74.5215.415.1–15.84.55FM (kg)12.211.9–12.64.6812.312.1–12.54.6512.311.9–12.74.92FFM (kg)65.565.0–66.06.4365.465.1–65.76.3165.665.1–66.16.86 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 2 Basic anthropometric characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDAge (years)37.336.6–38.09.1337.135.9–38.49.5037.636.5–38.88.46Height (cm)179.9179.4–180.46.27180.1179.2–181.06.96180.2179.4–181.06.13BM (kg)78.878.1–79.69.8079.177.7–80.510.479.878.4–81.310.9BMI (kg·m–2)24.324.1–24.62.6324.424.0–24.72.8024.624.2–25.02.96BF (%)16.415.7–17.14.9916.115.7–16.54.8116.215.5–16.84.87FM (kg)13.312.6–14.15.6613.012.6–13.45.2713.312.5–14.05.85FFM (kg)65.864.9–66.66.2565.865.4–66.36.0666.665.7–67.46.58 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 3 Cardiopulmonary exercise testing (CPET) characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)38.438.1–38.85.0138.538.3–38.74.8838.137.7–38.55.16RERAT0.870.86–0.870.040.870.86–0.870.040.870.86–0.870.04HRAT (beats·min–1)151.5150.8–152.310.3151.0150.6–151.510.8152.0151.2–152.810.8VEAT (L·min–1)79.178.1–80.012.278.377.8–78.912.077.276.3–78.212.0SPEEDAT (km·h–1)11.010.9–11.11.4511.011.0–11.11.3610.910.8–11.01.42LAAT (mmol·L–1)2.082.02–2.140.631.801.76–1.830.622.352.27–2.420.72rVO2RCP (mL·min–1·kg–1)47.547.0–48.05.8847.747.4–48.06.1547.346.8–47.86.16RERRCP1.001.00–1.000.041.001.00–1.000.041.001.00–1.000.03HRRCP (beats·min–1)173.4172.7–174.19.21173.2172.8–173.69.30174.3173.5–175.09.50VERCP (L·min–1)114.7113.5–116.015.9113.9113.1–114.616.7112.7111.4–114.016.2SPEEDRCP (km·h–1)14.013.9–14.11.7714.114.0–14.11.7013.913.8–14.11.75LARCP (mmol·L–1)4.724.63–4.821.044.404.34–4.451.044.814.69–4.931.14rVO2max (mL·min–1·kg–1)53.853.3–54.36.6754.354.0–54.66.9553.853.3–54.37.09 CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; SPEEDAT, velocity at anaerobic threshold; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; SPEEDRCP, velocity at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; rVO2max, maximal oxygen uptake relative to body mass. Table 4 Cardiopulmonary exercise testing (CPET) characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)33.032.5–33.45.8433.232.4–33.95.6833.732.9–34.55.89RERAT0.870.87–0.870.040.870.87–0.880.040.870.87–0.880.04HRAT CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; power at anaerobic threshold relative to body mass; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; power at respiratory compensation point relative to body mass; rVO2max, maximal oxygen uptake relative to body mass. selection variables were in the further only selected parameters were into multiple linear regression The data for MLR model building were randomly into that is testing, validation and of the a only significant were in the Derived are by the of mean and mean analysis was used to the model’s precision and accuracy during validation and tests to the fulfilment of MLR test the of in MLR test assessment between and test of Each model was examined the and any have not been 2 package in RStudio (R Core Team, Vienna, Austria; version version for and software version were used in was considered as the Results Somatic measurements and CPET results data of the runners models for testing, and validation are in Table while cyclists are in Table The runners of and for testing, and validation the cyclists and differences between of runners and cyclists were in BMI and between testing in all between validation only in CPET results for runners models are in Table 3 and for cyclists in Table Runners in the cohort achieved relative to body mass VO2max of in testing group and in validation group cyclists mean was and for testing, and validation to body mass oxygen uptake at anaerobic threshold in runners for ± ± and ± of in testing, and validation it was ± ± and ± of rVO2max, relative to body mass oxygen uptake at respiratory compensation point in runners for ± ± and ± of for testing, and validation while in cyclists for ± ± and ± of rVO2max, There were no significant differences in values between testing, and validation the runners and cyclists between runners and cyclists results were all significant Prediction models based on AT and RCP Full of MLR prediction models for cyclists are in Table for runners in Table The models prediction performance is as with and for cyclists from for somatic parameters to for RCP equations. For runners from for to for AT and equations. for cyclists models was the for RCP and the highest for For from for AT and to for equation. observed for cyclists was the for RCP in the validation group and the highest for while in runners the for AT and and the highest for The performance of prediction is in Figure Figure 2 Download asset Open asset of prediction for Abbreviations: maximal oxygen anaerobic threshold; RCP, respiratory compensation point; All values are in performance for running while the performance for cycling equations. performance of the prediction model for for for AT and for somatic-only equation. Table 5 VO2max prediction for cyclists. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass power at anaerobic threshold relative to body mass rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass VERCP, pulmonary ventilation at respiratory compensation point BF, body fat BM, body mass Table VO2max prediction for runners. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass SPEEDAT, velocity at anaerobic threshold FFM, fat mass VEAT, pulmonary ventilation at anaerobic threshold HRAT, heart rate at anaerobic threshold BF, body fat rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass SPEEDRCP, velocity at respiratory compensation point Models validation of each model for cyclists is in Table while for runners in Table the performance of our prediction was to that observed in the

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.

With continual changes made and reviews of the exchange rate regime of Solomon Islands it is imperative that a proper forecasting modelling tool is established. The use of neural network models in exchange rate forecasting has received much attention in recent research. In this paper we propose an artificial neural network (ANN) model for forecasting exchange rates of the Solomon Islands dollar (SBD) against Euro (EUR). We use daily exchange rate data during the period of January 5, 1998 to June 30, 2014. The proposed model is compared with a naive method as a benchmarked method. Further, it is compared with single exponential smoothing; double exponential smoothing with trend; and Holt-Winter multiplicative and additive seasonal and multiple linear regression models. The performance of the models was measured by using various error functions such as root mean square error, mean absolute error, and mean absolute percentage error. The validation tests of the models were also carried out using different goodness of fit measures such as R-square, bias and tracking signal. The empirical result reveals that the proposed model is an efficient tool for forecasting SBD against Euro more accurately than are regression and time series models.

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.

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&gt; 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 &amp; Sons, Ltd.

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

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.

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.

Meteorological conditions and other gaseous pollutants generally impacted the development of ozone (O3) in the atmosphere.The purpose of this study was to create the best O3model for forecasting O3concentrations in the industrial area and to determine the variables that affect O3concentrations.Five-year data of meteorological and gaseous pollutants were used to analyze and develop the prediction model. Based on three distinct techniques, three separate multiple linear regression (MLR) prediction models of O3concentration were developed.MLR3had the highest correlation coefficient of 0.792 during development as compared to models MLR1and MLR2. MLR2was deemed the best O3 prediction model, however, since it had the lowest error values of root mean square error (3.976) and mean absolute error (3.548) when compared to other models.The establishment of an O3prediction model can offer local governments with early information that could help them reduce and manage air pollution emissions.

The aim of this study is to assess the possibility of forecasting water level fluctuations in a relatively small (&amp;lt;100 km2), post-glacial lake located in a temperate climate zone by means of artificial neural networks and multiple linear regression. The area of study was Lake Serwy, located in northeastern Poland. Two artificial neural network (ANN) multilayer perceptron (MLP) and multiple linear regression (MLR) models were built. The following explanatory variables were considered: maximal and minimal temperature (Tmax, Tmin) wind speed (WS), vertical circulation (VC) and water level from previous periods (WL). Additionally, a binary variable describing the period of the year (winter, summer) has been considered in one of the two MLP and MLR models. The forecasting models have been assessed based on selected criteria: mean absolute percentage error (MAPE), root mean squared error (RMSE), coefficient of determination (R2) and mean biased error. Considering their values and absolute deviations from observed values it was concluded that the ANN model using an additional binary variable (MLP_B+) has the best forecasting performance. Absolute deviations from observed values were the determining factor which made this model the most efficient. In the case of the MLP_B+ model, those values were about 10% lower than in other models. The conducted analyses indicated good performance of ANN networks as a forecasting tool for relatively small lakes located in temperate climate zones. It is acknowledged that they enable water level forecasting with greater precision and lower absolute deviations than the use of multiple linear regression models.

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

The demand for healthcare facilities in the world is growing daily, and this growth in demand exceeds general population growth. This situation has made hospital trips a vital issue during urban transportation planning. In this context, the aim of this study is twofold: (1) to investigate the hospital trip behavior as home-based hospital trips within the scope of trip production and attraction (trip generation) models and (2) to evaluate the predictive power of some robust and regularization methods in trip generation modeling. Within this scope, approximately 49,000 valid Household Survey Data (HSD) from 2001 (base year) and 2015 (target year) were used to develop comprehensive trip generation models for the home-based hospital trips. Multiple linear regression (MLR), ridge regression (RR), Liu, least trimmed squares (LTS), least trimmed squares–ridge (LTS–R), and least trimmed square–Liu (LTS–L) methods were used for the analysis, and results were evaluated in terms of specialized mean squared error (MSE) and root mean square error (RMSE). As a result, LTS–R and LTS–L increased future predictive power by approximately 55% compared with OLS. This study fills an important gap in the literature in terms of not only the use of regularization and robust methods in trip demand modeling but also examining characteristics that affect hospital trip behaviors. In addition, the paper proposes a “Hospital Mobility Coefficient” projection that could be useful in demand estimation for future hospital trips.