Simple Linear Equations to Estimate a Workload of Specific Repetition Maximum for Squat Exercise in Trained and Untrained Males

Background: Suicide remains a leading cause of death among youth, yet effective tools to predict suicide attempts (SA) in individuals under 18 are scarce. This study aims to develop machine learning (ML) models to predict SA in paediatric populations using Google Trends data. Methods: Relative Search Volumes (RSVs) from Google Trends were analysed for terms linked to suicide risk factors. Pearson Correlation Coefficients (PCC) identified terms strongly associated with SA rates. Based on these, several ML models were developed and evaluated, including Random Forest Regression, Support Vector Regression (SVR), XGBoost, and Linear Regression. Model performance was assessed using metrics such as PCC, mean absolute error (MAE), mean squared error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE). Results: Terms related to suicide prevention and symptoms, including psychiatrist and anxiety disorder, showed the strongest correlations with SA rates (PCC ≥ 0.90). Random Forest Regression emerged as the top-performing ML model (PCC = 0.953, MAPE = 20.12%, RMSE = 17.21), highlighting burnout, anxiety disorder, antidepressants, and psychiatrist as key predictors of SA. Other models’ scores were XGBoost (PCC = 0.446, MAPE = 22.57%, RMSE = 18.03), SVR (PCC = 0.833, MAPE = 42.23%, RMSE = 47.32) and Linear Regression (PCC = 0.947, MAPE = 23.64%, RMSE = 17.66). Conclusions: Google Trends–based ML models suggest potential utility for short-term prediction of youth SA. These preliminary findings support the utility of search data in identifying real-time suicide risk in paediatric populations.

Globally, wind energy if properly harnessed, could serve as a source of energy generation in Africa. This study compared the performance of two Machine Learning (ML) algorithms (Linear regression and Random Forest) in predicting wind speed in five major cities in Africa (Yaoundé, Pretoria, Nairobi, Cairo and Abuja). Wind data were collected between January 1, 2000, and December 31, 2022, using the Solar Radiation Data Archive. The data preprocessing was carried out with 80% of the data used for training and 20% for validation. The performance of these ML algorithms was evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and coefficient of determination (R2). The result shows that Nairobi (3.814795 m/s) closely followed by Cairo (3.606453 m/s) has the highest mean wind speed while Yaoundé (1.090512 m/s) has the lowest. Based on the performance metrics used, the two Machine Learning algorithms were competitive. Still, the Linear Regression (LR) algorithm outperformed the Random Forest Algorithm in predicting wind speed in all the selected major African cities. In Yaoundé (RMSE = 0.3892, MAE= 0.3001, MAPE =0.5030), Pretoria (RMSE=1.2339, MAE=0.9480, MAPE=0.7450) Nairobi (RMSE= 0.4223, MAE =0.6499, MAPE =0.1872), Nairobi (RMSE=0.6499, MAE=0.5171, MAPE =0.1872), Cairo (RMSE =1.0909, MAE =0.8544, MAPE =0.3541) and Abuja (RMSE = 0.70245, MAE =0.5441, MAPE= 0.4515) the Linear regression algorithms was found to outperformed Random Forest Regression. Therefore, the Linear regression algorithm is more reliable in predicting wind speed compared with the Random Forest regression.

BackgroundStress fractures are injuries caused by repetitive loading during activities such as running. The application of advanced analytical methods such as machine learning to data from multiple wearable sensors has allowed for predictions of biomechanical variables associated with running-related injuries like stress fractures. However, it is unclear if data from a single wearable sensor can accurately estimate variables that characterize external loading during running such as peak vertical ground reaction force (vGRF), vertical impulse, and ground contact time. Predicting these biomechanical variables with a single wearable sensor could allow researchers, clinicians, and coaches to longitudinally monitor biomechanical running-related injury risk factors without expensive force-measuring equipment.PurposeWe quantified the accuracy of applying quantile regression forest (QRF) and linear regression (LR) models to sacral-mounted accelerometer data to predict peak vGRF, vertical impulse, and ground contact time across a range of running speeds.MethodsThirty-seven collegiate cross country runners (24 females, 13 males) ran on a force-measuring treadmill at 3.8–5.4 m/s while wearing an accelerometer clipped posteriorly to the waistband of their running shorts. We cross-validated QRF and LR models by training them on acceleration data, running speed, step frequency, and body mass as predictor variables. Trained models were then used to predict peak vGRF, vertical impulse, and contact time. We compared predicted values to those calculated from a force-measuring treadmill on a subset of data (n = 9) withheld during model training. We quantified prediction accuracy by calculating the root mean square error (RMSE) and mean absolute percentage error (MAPE).ResultsThe QRF model predicted peak vGRF with a RMSE of 0.150 body weights (BW) and MAPE of 4.27 ± 2.85%, predicted vertical impulse with a RMSE of 0.004 BW*s and MAPE of 0.80 ± 0.91%, and predicted contact time with a RMSE of 0.011 s and MAPE of 4.68 ± 3.00%. The LR model predicted peak vGRF with a RMSE of 0.139 BW and MAPE of 4.04 ± 2.57%, predicted vertical impulse with a RMSE of 0.002 BW*s and MAPE of 0.50 ± 0.42%, and predicted contact time with a RMSE of 0.008 s and MAPE of 3.50 ± 2.27%. There were no statistically significant differences between QRF and LR model prediction MAPE for peak vGRF (p = 0.549) or vertical impulse (p = 0.073), but the LR model’s MAPE for contact time was significantly lower than the QRF model’s MAPE (p = 0.0497).ConclusionsOur findings indicate that the QRF and LR models can accurately predict peak vGRF, vertical impulse, and contact time (MAPE < 5%) from a single sacral-mounted accelerometer across a range of running speeds. These findings may be beneficial for researchers, clinicians, or coaches seeking to monitor running-related injury risk factors without force-measuring equipment.

IntroductionIn recent years, load-velocity profiles (LVP) have been frequently proposed as a highly reliable and valid alternative to the one-repetition maximum (1RM) for estimating maximal strength and prescribing training loads. However, previous authors commonly report intraclass correlation coefficients (ICC) while neglecting to calculate the measurement error associated with these values. This is important for practitioners, especially in an elite sports setting, to be able to differentiate between small but significant changes in performance and the error rate.Methods49 youth elite athletes (17.71±2.07 years) were recruited and performed a 1RM test followed by a load-velocity profiling test using 30%, 50% and 70% of the 1RM in the bench press and bench pull, respectively. Reliability analysis, ICCs and the coefficient of variability, were calculated and supplemented by an agreement analysis including the mean absolute error (MAE) and mean absolute percentage error (MAPE) to provide the resulting measurement error. Furthermore, validity analyses between the measured 1RM and different calculation models to estimate 1RM were performed.ResultsReliability values were in accordance with current literature (ICC = 0.79–0.99, coefficient of variance [CV] = 1.86–9.32%), however, were accompanied by a random error (mean absolute error [MAE]: 0.05–0.64 m/s, mean absolute percentage error [MAPE]: 2.7–9.5%) arising from test-retest measurement. Strength estimation via the velocity-profile overestimated the bench pull 1RM (limits of agreement [LOA]: -9.73 – -16.72 kg, MAE: 9.80–17.03 kg, MAPE 16.9–29.7%), while the bench press 1RM was underestimated (LOA: 3.34–6.37 kg, MAE: 3.74–7.84 kg, MAPE: 7.5–13.4%); dependent on used calculation model.DiscussionConsidering the observed measurement error associated with LVP-based methods, it can be posited that their utility as a programming strategy is limited. The lack of accuracy required to discriminate between small but significant changes in performance and error, coupled with the potential risks of under- and overestimating 1RM, can result in insufficient stimulus or increased injury risk, respectively. This further diminishes the practicality of these methods, particularly in elite sports settings.

Measuring maximal strength (MSt) is a very common performance diagnoses, especially in elite and competitive sports. The most popular procedure in test batteries is to test the one repetition maximum (1RM). Since testing maximum dynamic strength is very time consuming, it often suggested to use isometric testing conditions instead. This suggestion is based on the assumption that the high Pearson correlation coefficients of r ≥ 0.7 between isometric and dynamic conditions indicate that both tests would provide similar measures of MSt. However, calculating r provides information about the relationship between two parameters, but does not provide any statement about the agreement or concordance of two testing procedures. Hence, to assess replaceability, the concordance correlation coefficient (ρ c) and the Bland-Altman analysis including the mean absolute error (MAE) and the mean absolute percentage error (MAPE) seem to be more appropriate. Therefore, an exemplary model based on r = 0.55 showed ρ c = 0.53, A MAE of 413.58 N and a MAPE = 23.6% with a range of -1,000-800 N within 95% Confidence interval (95%CI), while r = 0.7 and 0.92 showed ρ c = 0.68 with a MAE = 304.51N/MAPE = 17.4% with a range of -750 N-600 N within a 95% CI and ρ c = 0.9 with a MAE = 139.99/MAPE = 7.1% with a range of -200-450 N within a 95% CI, respectively. This model illustrates the limited validity of correlation coefficients to evaluate the replaceability of two testing procedures. Interpretation and classification of ρ c, MAE and MAPE seem to depend on expected changes of the measured parameter. A MAPE of about 17% between two testing procedures can be assumed to be intolerably high.

Accurately measured or estimated reference evapotranspiration (ETo) data are needed to properly manage water resources and prioritise their future uses. ETo can be most accurately measured using lysimeter systems. However, high installation and operating costs, as well as difficult and time-consuming measurement processes limit the use of these systems. Therefore, the approach of estimating ETo by empirical models is more preferred and widely used. However, since those models are well in accordance with the climatic and environmental traits of the region in which they were developed, their reliability must be examined if they are utilised in distinctive regions. This study aims to test the usability of mass transfer-based Dalton, Rohwer, Penman, Romanenko, WMO and Mahringer models in Van Lake microclimate conditions and to calibrate them in compatible with local conditions. Firstly, the original equations of these models were tested using 9 years of daily climate data measured between 2012 and 2020. Then, the models were calibrated using the same data and their modified equations were created. The original and modified equations of the models were also tested with the 2021 and 2022 current climate data. Modified equations have been created using the Microsoft Excel program solver add-on, which is based on linear regression. The daily average ETo values estimated using the six mass transfer-based models were compared with the daily average ETo values calculated using the standard FAO-56 PM equation. The statistical approaches of the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), Nash-Sutcliffe Efficiency (NSE), and determination coefficient (R2) were used as comparison criterion. The best and worst performing models in the original equations were Mahringer (MAE = 0.70 mm day-1, MAPE = 15.86%, RMSE = 0.87 mm day-1, NSE = 0.81, R2 = 0.94) and Penman (MAE = 1.84 mm day-1, MAPE = 33.68%, RMSE = 2.39 mm day-1, NSE = -0.49, R2 = 0.91), respectively, whereas in the modified equations Dalton (MAE = 0.29 mm day-1, MAPE = 7.51%, RMSE = 0.33 mm day-1, NSE = 0.97, R2 = 0.97) and WMO (MAE = 0.36 mm day-1, MAPE = 8.89%, RMSE = 0.43 mm day-1, NSE = 0.95, R2 = 0.97). The RMSE errors of the daily average ETo values estimated using the modified equations were generally below the acceptable error limit (RMSE < 0.50 mm day-1). It has been concluded that the modified equations of the six mass transfer-based models can be used as alternatives to the FAO-56 PM equation under the Van Lake microclimate conditions (NSE > 0.75), while the original equations-except for those of Mahringer (NSE = 0.81), WMO (NSE = 0.79), and Romanenko (NSE = 0.76)-cannot be used.

Long-term load forecasting based on adaptive neural fuzzy inference system using real energy data

Lung transplantation is the standard treatment for end-stage lung diseases. A crucial factor affecting its success is size matching between the donor's lungs and the recipient's thorax. Computed tomography (CT) scans can accurately determine recipient's lung size, but donor's lung size is often unknown due to the absence of medical images. We aim to predict donor's right/left/total lung volume, thoracic cavity, and heart volume from only subject demographics to improve the accuracy of size matching. A cohort of 4610 subjects with chest CT scans and basic demographics (i.e., age, gender, race, smoking status, smoking history, weight, and height) was used in this study. The right and left lungs, thoracic cavity, and heart depicted on chest CT scans were automatically segmented using U-Net, and their volumes were computed. Eight machine learning models [i.e., random forest, multivariate linear regression, support vector machine, extreme gradient boosting (XGBoost), multilayer perceptron (MLP), decision tree, -nearest neighbors, and Bayesian regression) were developed and used to predict the volume measures from subject demographics. The 10-fold cross-validation method was used to evaluate the performances of the prediction models. -squared ( ), mean absolute error (MAE), and mean absolute percentage error (MAPE) were used as performance metrics. The MLP model demonstrated the best performance for predicting the thoracic cavity volume ( : 0.628, MAE: 0.736L, MAPE: 10.9%), right lung volume ( : 0.501, MAE: 0.383L, MAPE: 13.9%), and left lung volume ( : 0.507, MAE: 0.365L, MAPE: 15.2%), and the XGBoost model demonstrated the best performance for predicting the total lung volume ( : 0.514, MAE: 0.728L, MAPE: 14.0%) and heart volume ( : 0.430, MAE: 0.075L, MAPE: 13.9%). Our results demonstrate the feasibility of predicting lung, heart, and thoracic cavity volumes from subject demographics with superior performance compared with available studies in predicting lung volumes.

To compare the application of the ARIMA model, the Long Short-Term Memory (LSTM) model and the ARIMA-LSTM model in forecasting foodborne disease incidence. Monthly case data of foodborne diseases in Liaoning Province from January 2015 to December 2023 were used to construct ARIMA, LSTM, and ARIMA-LSTM models. These three models were then applied to forecast the monthly incidence of foodborne diseases in 2024, and their predictions were compared with those of a baseline model. Model performance was evaluated by comparing the predicted and observed values using root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), allowing identification of the optimal model. The best-performing model was subsequently employed to predict the monthly incidence for 2025. The ARIMA-LSTM model was identified as the optimal model. Specifically, the ARIMA (2,0,0) (0,1,1)12 model produced RMSE = 300.03, MAE = 187.11, and MAPE = 16.38%, while the LSTM model yielded RMSE = 408.71, MAE = 226.03, and MAPE = 17.21%. In contrast, the ARIMA-LSTM model achieved RMSE = 0.44, MAE = 0.44, and MAPE = 0.08%, representing a dramatic improvement over the baseline model (RMSE = 204.17, MAE = 146.75, MAPE = 15.62%), with reductions of 99.5%, 99.7%, and 99.4% in RMSE, MAE, and MAPE, respectively. Based on the ARIMA-LSTM model, the predicted monthly cases of foodborne diseases for 2025 are: 214.62 (Jan), 260.84 (Feb), 462.92 (Mar), 590.92 (Apr), 800.88 (May), 965.11 (Jun), 2410.36 (Jul), 2651.36 (Aug), 1711.15 (Sep), 941.22 (Oct), 628.21 (Nov), and 465.05 (Dec). The ARIMA-LSTM model is considered the optimal model for predicting foodborne disease incidence in Liaoning Province in 2025.

Target population estimation for immunization coverage calculations from census data is often inaccurate. This study aimed to evaluate the accuracy of the traditional census extrapolation method in comparison with three alternative approaches: the Cohort-Component Population Projections Method (CCPPM), using the Expanded Program on Immunisation (EPI) numerators - BCG and DTP1 doses as denominators, and estimates derived from first antenatal care clinic (ANC1) visits. We obtained target population estimates in Kenya from 1999 - 2023 using all 4 methods with data for ANC1 available only for 2020-2023. We assessed the accuracy of the estimates for 2003-2018 by computing the Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and the Pearson Correlation Coefficient (r), excluding outliers. A sub-analysis for the period 2020-2023 included ANC1 data. The CCPPM method had the largest population estimates while the census-based method had pronounced discontinuities at the census years. The CCPPM method compared to the DTP1 doses was associated with the greatest error magnitude (MAE = 212917.19 and MAPE = 18.18) while the DTP1 doses and census-based methods showed the smallest error (MAE = 44317.16 and MAPE = 3.77). Sub-analysis of target populations for the period 2020-2023 showed similar upward trends except for the census-based method which exhibited a significantly divergent trajectory. Comparison between the ANC1 and DTP1 doses showed the strongest linear correlation (r = 1.00). Although sub-national analysis was not done and there was the significant challenge of missing data, the results nevertheless reveal significant inaccuracies in the current target population estimation methods which may have serious implications on immunisation coverage assessments. Immunisation programs should utilise diverse sources of data and triangulate results as a more pragmatic approach for approximating the target populations for vaccination in the absence of well-established civil registration systems. Additionally, more research is warranted to address this gap.

BackgroundInfluenza in mainland China results in a large number of outpatient and emergency visits related to influenza-like illness (ILI) annually. While deep learning models show promise for improving influenza forecasting, their technical complexity remains a barrier to practical implementation. Large language models, such as ChatGPT, offer the potential to reduce these barriers by supporting automated code generation, debugging, and model optimization.ObjectiveThis study aimed to evaluate the predictive performance of several deep learning models for ILI positive rates in mainland China and to explore the auxiliary role of ChatGPT-assisted development in facilitating model implementation.MethodsILI positivity rate data spanning from 2014 to 2024 were obtained from the Chinese National Influenza Center (CNIC) database. In total, 5 deep learning architectures—long short-term memory (LSTM), neural basis expansion analysis for time series (N-BEATS), transformer, temporal fusion transformer (TFT), and time-series dense encoder (TiDE)—were developed using a ChatGPT-assisted workflow covering code generation, error debugging, and performance optimization. Models were trained on data from 2014 to 2023 and tested on holdout data from 2024 (weeks 1‐39). Performance was evaluated using mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).ResultsILI trends exhibited clear seasonal patterns with winter peaks and summer troughs, alongside marked fluctuations during the COVID-19 pandemic period (2020‐2022). All 5 deep learning models were successfully constructed, debugged, and optimized with the assistance of ChatGPT. Among the 5 models, TiDE achieved the best predictive performance nationally (MAE=5.551, MSE=43.976, MAPE=72.413%) and in the southern region (MAE=7.554, MSE=89.708, MAPE=74.475%). In the northern region, where forecasting proved more challenging, TiDE still performed best (MAE=4.131, MSE=28.922), although high percentage errors remained (MAPE>400%). N-BEATS demonstrated the second-best performance nationally (MAE=9.423) and showed greater stability in the north (MAE=6.325). In contrast, transformer and TFT consistently underperformed, with national MAE values of 10.613 and 12.538, respectively. TFT exhibited the highest deviation (national MAPE=169.29%). Extreme regional disparities were observed, particularly in northern China, where LSTM and TFT generated MAPE values exceeding 1918%, despite LSTM’s moderate performance in the south (MAE=9.460).ConclusionsDeep learning models, particularly TiDE, demonstrate strong potential for accurate ILI forecasting across diverse regions of China. Furthermore, large language models like ChatGPT can substantially enhance modeling efficiency and accessibility by assisting nontechnical users in model development. These findings support the integration of AI-assisted workflows into epidemic prediction systems as a scalable approach for improving public health preparedness.

We have demonstrated that machine learning allows us to predict cognitive function in aged people using near-infrared spectroscopy (NIRS) data or basic blood test data. However, the following points are not yet clear: first, whether there are differences in prediction accuracy between NIRS and blood test data; second, whether there are differences in prediction accuracy for cognitive function in linear models and non-linear models; and third, whether there are changes in prediction accuracy when both NIRS and blood test data are added to the input layer. We used a linear regression model (LR) for the linear model and random forest (RF) and deep neural network (DNN) for the non-linear model. We studied 250 participants (mean age = 73.3 ± 12.6 years) and assessed cognitive function using the Mini Mental State Examination (MMSE) (mean MMSE scores = 22.9 ± 6.1). We used time-resolved NIRS (TNIRS) to measure absolute concentrations of hemoglobin and optical pathlength at rest in the bilateral prefrontal cortices. A basic blood test was performed on the same day. We compared predicted MMSE scores and grand truth MMSE scores; prediction accuracies were evaluated using mean absolute error (MAE) and mean absolute percentage error (MAPE). We found that (1) the DNN-based prediction using TNIRS data exhibited lower MAE and MAPE compared with those using blood test data, (2) the difference in MAPE between TNIRS and blood test data was only 0.3%, (3) adding TNIRS data to the blood test data of the input layer only improved MAPE by 1.0% compared to the use of blood test data alone, whereas the use of the blood test data alone exhibited the prediction accuracy with 81.8% sensitivity and 91.3% specificity (N = 202, repeated five-fold cross validation). Given these findings and the benefits of using blood test data (low cost and large-scale screening possible), we concluded that the DNN model using blood test data is still the most suitable for mass screening.

The objective of the industry in general, and of the chemical industry in particular, is to satisfy consumer demand for products and the best way to satisfy it is to forecast future sales and plan its operations.Considering that the choice of the best sales forecast model will largely depend on the accuracy of the selected indicator (Tofallis, 2015), in this work, seven techniques are compared, in order to select the most appropriate, for quantifying the error presented by the sales forecast models. These error evaluation techniques are: Mean Percentage Error (MPE), Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Absolute Scaled Error (MASE), Symmetric Mean Absolute Percentage Error (SMAPE) and Mean Absolute Arctangent Percentage Error (MAAPE). Forecasts for chemical product sales, to which error evaluation techniques are applied, are those obtained and reported by Castillo, et. al. (2016 &amp; 2020).The error measuring techniques whose calculation yields adequate and convenient results, for the six prediction techniques handled in this article, as long as its interpretation is intuitive, are SMAPE and MAAPE. In this case, the most adequate technique to measure the error presented by the sales prediction system turned out to be SMAPE.

The main purpose of the sheep production is to improve profitability of yield traits such as meat, milk and wool obtained per animal. In this respect, selection is a remarkable tool for achieving genetic improvement and attaining better qualified offspring as to the quantitative traits. In obtaining of superior offspring according to a quantitative trait like live weight, the conservation of indigenous genetic sources and the detection of the breed standards, animal breeders take into account indirect selection criteria with the help of high genetic correlation coefficients between live weight and morphological traits. Moreover, the prediction of live body weight from some zoometrical (morphological) characteristics measured simply in farm animals is an important subject for developing prosperous animal breeding systems and in practice, regulating management conditions [1; 2]. A simple way to find out appropriate feed amount, medicinal dose and price of an animal farm is to predict live body weight from effective morphological traits. The predictive accuracy depends on choosing powerful statistical approaches. Among those, there is multiple linear regression, which leads analysts to make biased parameter estimates with multicollinearity problem occurring as an outcome of very strong Pearson correlation coefficients between morphological traits as predictors of body weight [3]. A good alternative is, in general, to use Ridge Regression Analysis instead. However, Ridge regression can produce unreliable outcomes [4]. More effective alternatives to remove multicollinearity problem are available, such as using scores of factor analysis and principal component analysis for multiple regression analysis technique [5; 6]. Predictors are exposed to factor or principal component analysis as one of multivariate analysis techniques and new uncorrelated predictors are used to predict the body weight without multicollinearity problem [6].Recent studies show that the most effective alternatives in the body weight prediction are data mining algorithms. Among these algorithms, CART (Classification and Regression Tree), CHAID (Chi-Square Automatic Interaction Detector) and Exhaustive CHAID construct a regression tree structure that can be interpreted easily by researchers. CART tree-based algorithm recursively products binary splits by partitioning a subset into two small subsets until achieving the strongest Pearson coefficient in body weight trait between observed and predicted values. CHAID algorithm recursively uses multi-way splitting in regression tree construction for the strongest Pearson coefficient as a model quality criterion [7]. In the CHAID algorithms, there are three stages, merging, splitting and stopping and the Bonferroni adjusment is available in the estimation of adjusted P values. The last two stages are the same; however, Exhaustive CHAID algorithm employs an exhaustive procedure in order to merge any similar pairs until obtaining merely a single pair in regression tree structure. CHAID algorithms implement F significance test when a response variable (body weight) is continuous. In this situation, the tree diagram constructed for a continuous response variable in CART and both CHAID algorithms is called the regression tree, otherwise named as the classification tree. CHAID algorithms become automatically active to prune the redundant structures in the regression tree diagram. However, in the CART algorithm, analysts should activate a pruning option. Usability of Artificial Neural Networks (ANNs) algorithms as more sophisticated approaches in the prediction of body weight is scarce [7]. To reveal the complicated relationship between a response variable (body weight) and other input variables (predictors), ANNs, functioning like human brain and consisting of input, hidden and output layers, are the best choice. However, it is extremely difficult to interpret their outputs compared with the tree-based data mining algorithms. In this respect, ANNs are also called as black boxes.For researchers who aim to predict an equation for body weight, application of MARS (Multivariate Adaptive Regression Splines) data mining algorithm which is unavailable in literature should be preferred. More importantly, MARS, a non-parametric regression statistical technique to get linear piecewise functions and to evaluate high order interactions between predictors, is used to reveal more complex relationships between sets of more-than-one dependent variables and predictors with the aid of pruning option. Compared to other statistical approaches mentioned above, MARS provides a much higher predictive performance in prediction problems. For this reason, MARS can be applied to RSM data consisting of more-than-one dependent variables and predictors in agricultural and medical sciences. This type of application is absent in literature.Several model evaluation criteria are recommended in testing and comparing predictive performances of the statistical approaches addressed above [7].a) Pearson correlation coefficient (r) between the actual and predicted BW values,b) Root-mean-square error (RMSE)c) Mean error (ME) given by the following equation:d) Mean absolute deviation (MAD):e) Standard deviation ratio (SDratio):f) Global relative approximation error (RAE):g) Mean absolute percentage error (MAPE):h) Coefficient of Determinationi) Adjusted Coefficient of Determination Where:n is the number of animals in a set, k is the number of model parameters, yi is the observed value of a response variable (Body weight), yip is the predicted value of the response variable (Body weight), sm is the standard deviation of the model residuals, sd is the standard deviation of the response variable (Body weight) and is the mean of the response variable (Body weight).The best model should have the greatest Pearson coefficient, R2 and adjusted R2 and the lowest RMSE, MAD, MAPE and RAE. SD ratio should become equal to the value less than 0.40 for a good fit in model, and for very good fit, the ratio should be equal to the value less than 0.10 [7].Consequently, researchers generally prefer more understandable and interpretable statistical approaches. In the scope of regression analysis, the most fundamental purpose is to minimize residuals expressed as differences in body weight between observed and predicted values or to maximize Pearson correlation coefficient between observed and predicted values, obtained by statistical analysis approach, in the body weight.

Omcirk, D, Vetrovsky, T, Padecky, J, Malecek, J, and Tufano, JJ. Validity of commercially available punch trackers. J Strength Cond Res 37(11): 2273-2281, 2023-This study determined how well data from commercially available punch trackers (Corner, Hykso, and StrikeTec) related to gold-standard velocity and force measures during full-contact punches. In a quasi-randomized order, 20 male subjects performed 6 individual rear straight punches, rear hooks, and rear uppercuts against a wall-mounted force plate. Punch tracker variables were compared with the peak force of the force plate and to the peak (QPV) and mean velocity (QMV) assessed through Qualisys 3-dimensional tracking. For each punch tracker variable, Pearson's correlation coefficient, mean absolute percentage error (MAPE), and mean percentage error (MPE) were calculated. There were no strong correlations between punch tracker data and gold-standard force and velocity data. However, Hykso "velocity" was moderately correlated with QMV ( r = 0.68, MAPE 0.64, MPE 0.63) and QPV ( r = 0.61, MAPE 0.21, MPE -0.06). Corner Power G was moderately correlated with QMV ( r = 0.59, MAPE 0.65, MPE 0.58) and QPV ( r = 0.58, MAPE 0.27, MPE -0.09), but Corner "velocity" was not. StrikeTec "velocity" was moderately correlated with QMV ( r = 0.56, MAPE 1.49, MPE 1.49) and QPV ( r = 0.55, MAPE 0.46, MPE 0.43). Therefore, none of the devices fared particularly well for all of their data output, and if not willing to accept any room for error, none of these devices should be used. Nevertheless, these devices and their proprietary algorithms may be updated in the future, which would warrant further investigation.