Regression Equation Research Articles

Maximizing the number of allowable approximation errors when building a linear regression model

Subject of research: errors in approximation of a linear regression model within the framework of a logical-algebraic approach to data analysis. Purpose of the study: to develop an algorithmic method for solving the problem of maximizing the number of permissible approximation errors using a linear-Boolean programming computer. Methods and objects of research: the object of research is a linear regression model, the methods are linear regression analysis and mathematical programming apparatus. Main results of the study: an algorithmic method is proposed for maximizing the number of permissible absolute and relative errors in approximation of a linear regression equation, which reduces to solving linear-Boolean programming problems of a dimension acceptable for practical situations. Solving generated problems of this type should not cause computational problems due to a significant number of effective software tools, for example, the LPsolve program, which is freely available on the Internet.

Mediating role of resilience on burnout to well-being for hospital nursing staff in Northeast China: a cross-sectional study

ObjectivesThe well-being of nursing staff is closely related to nursing performance and patient safety. It has attracted much attention from nursing managers and researchers. However, the most important influencing factors...

The Agreement of Intraocular Pressure Measurement in Healthy Merinos Sheep Using Rebound Tonometer (Tonovet®) and Applanation Tonometer (Tono-Pen VetTM)

The assessment of intraocular pressure (IOP) holds significant importance in ophthalmology as a crucial diagnostic tool for various ocular disorders. In the realm of comparative ophthalmology research, investigating ocular examination in sheep, particularly Merinos, is of considerable interest. This study aimed to evaluate the agreement between rebound (TonoVet®, TV) and applanation (Tono-Pen Vet™, TPV) tonometers in measuring IOP in healthy Merino sheep. 155 healthy Merinos (80 males, 75 females) with a mean weight of 54.4 ± 8.7 kg, aged 24 ± 6 months, were included in the study. IOP was measured between 9:00 and 11:00 am using both the rebound and applanation tonometers. The rebound tonometer was utilized first, followed by the applanation tonometer. A total of 620 readings (310 readings per eye) were obtained from the two devices. No statistical differences were noted between the mean IOP measurements of the right and left eyes for both tonometers (P > 0.05). However, there was a significant difference in the mean IOP measurements between the TV (11.8 ± 2.3 mmHg) and the TPV (13.9 ± 2.9 mmHg) tonometers (P < 0.001). The concordance correlation coefficient indicated weak agreement strength (ρc = 0.319, CI 95% = -0.169 to 0.455) between the TV and TPV. The mean difference in bias and the 95% limits of agreement for the differences between TV and TPV were -2.1 mmHg (-9.0 to 3.5 mmHg). The regression equation derived from a Bland-Altman plot, describing the relationship between the two tonometers, was Y = 1.43 - 0.33X (Y = TV and X = TPV). In conclusion, the TPV measured higher IOP values compared to the TV, and due to the significant bias and limits of agreement, the two tonometers should not be used interchangeably for IOP measurement in Merino sheep.

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

Evaluation of Maize Seed Sieving Performance using Sieves with CassiniOval Shape Openings

The process of preliminary cleaning is a determining factor affecting the standard qualities of the seeds. The grain mass that undergoes primary processing contains significant amounts of impurities, the amount of which is strictly regulated by standards. Sieves with rectangular and round openings are the most widely used for separating maize seeds. In this study, the feasibility and efficiency of using sieves with openings in the Cassini oval shape were proposed and substantiated. Three factors subject to variation during the experiments were selected, each having a crucial influence on the process parameters: rotational speed (n, rpm), specific material feed (Q, kg), and angle of sieve inclination (α, deg.). A regression equation was developed, and the response surfaces of the dependencies of defining characteristics of the process of separation of maize seeds on sieves with openings in the Cassini oval shape were compiled and analyzed. The study showed that the rotational speed has a less significant influence on the mass of the undersize of sieved maize than the inclination angle and feeding rate. A maximum grain passage (2.9 kg) into the openings in the Cassini oval shape is obtained at a rotational speed of 290.35 min-1 and a grain feed rate of 3.06 kg min-1.

Image Features and Diagnostic Value of Contrast-Enhanced Ultrasound for Ductal Carcinoma In Situ of the Breast: Preliminary Findings.

To explore the image features and the diagnostic value of contrast-enhanced ultrasound (CEUS) for ductal carcinoma in situ (DCIS) of the breast. A total of 96 female patients with a solitary and histologically proven DCIS were analyzed retrospectively, and 100 female cases of invasive ductal carcinoma (IDC) lesions were used as the control group. The Breast Imaging Reporting and Data System (BI-RADS) category of breast lesions was assessed according to conventional ultrasound features. The DCIS lesions were classified into mass type and non-mass type. The CEUS characteristics of these breast lesions were retrospectively analyzed qualitatively and quantitatively. The final gold standard was biopsy or surgery with histo-pathological examination. Comparing the ultrasound images of DCIS with that of IDC, there were significant differences in echo pattern, calcification morphology, and calcification distribution (p < .05 for all). There was a significant difference between DCIS and IDC in enhancement intensity, perfusion defects, peripheral high enhancement, intratumoral vessels, and arrival time (AT) (p < .05 for all). In the logistic multivariate regression analysis, two indicators linked with DCIS were recognized: perfusion defects (p = .002) and peripheral high enhancement (p < .001). In forecasting DCIS, the logistic regression equation resulted in an AUC of 0.689, a specificity of 0.720, and a sensitivity of 0.563. CEUS showed differences in enhancement characteristics between DCIS and IDC, with perfusion defects and peripheral high enhancement being associated with DCIS.

Exploring the correlation between airborne pollen levels and respiratory conditions in Jaipur, India

ABSTRACT Airborne pollen, a significant natural pollutant, restricts outdoor activities and impacts quality of life for sensitive individuals with pulmonary disorders. This study examines trends in airborne pollen concentrations and explores whether air pollution, pollen concentration, or both impact patient counts. The annual pollen trend in Jaipur shows peaks in pollen concentration in March (due to trees, 66%), September (due to weeds, 45%), and December (due to grass, 50%). Among the fifteen taxa examined, Holoptelea integrifolia is the largest pollen emitter in Jaipur, followed by Poaceae, among others. The count of patients arriving for clinical consultations in a hospital shows a strong and positive correlation with weed (Asteraceae spp. and Argemone mexicana) and grass pollen. A linear regression equation is developed (R2 value = 0.835) for forecasting consulting patient counts based on Cassia siamea pollen concentration. This can assist hospital administration in resource management, especially during peak allergy seasons.

Strengths mindset and job satisfaction: The mediating role of thriving at work and the moderating role of authentic leadership

We examined whether thriving at work mediated the relationship between strengths mindset and job satisfaction, as well as the moderating role of authentic leadership within this relationship. Data were gathered from 717 employees (female = 46%; mean age = 31.77 years, SD = 4.23 years) working in various organisations (including industries such as manufacturing, energy, and education) in China at two points in time with a two-week interval (time 1: n = 798, time 2: n = 717). Regression equation models indicated that strengths mindset was associated with job satisfaction. Thriving at work fully mediated the positive association between strengths mindset and job satisfaction, resulting in higher job satisfaction. Furthermore, authentic leadership positively moderated the direct and indirect effect of strengths mindset on thriving at work resulting in higher job satisfaction. Consistent with trait activation theory and socially-embedded model of thriving, strengths mindset and job satisfaction may provide managers with valuable strategies to enhance employees’ work wellbeing.

Isotonic subgroup selection

Abstract Given a sample of covariate–response pairs, we consider the subgroup selection problem of identifying a subset of the covariate domain where the regression function exceeds a predetermined threshold. We introduce a computationally feasible approach for subgroup selection in the context of multivariate isotonic regression based on martingale tests and multiple testing procedures for logically structured hypotheses. Our proposed procedure satisfies a non-asymptotic, uniform Type I error rate guarantee with power that attains the minimax optimal rate up to poly-logarithmic factors. Extensions cover classification, isotonic quantile regression, and heterogeneous treatment effect settings. Numerical studies on both simulated and real data confirm the practical effectiveness of our proposal, which is implemented in the R package ISS.

Technological line for the production of sunflower cake

BACKGROUND: The results of the study conducted to increase the shelf life of sunflower cake by justifying the optimal operating parameters of the ozonizer in the line of the sunflower cake production are presented. Studies of the processing of sunflower cake with an ozone-air mixture at optimal operating parameters, such as its concentration, the duration of its processing and the intensity of the high-frequency field, have been conducted. AIM: Increasing of the long-term storage of protein feed by improving the basic design parameters of the device for its production. METHODS: Resulting from the conducted theoretical research, the technological line for the protein feed production was developed according to the patent for the invention of the Russian Federation No. 2706188. To determine the optimal operating parameters of the device in the sunflower cake production line, which affect its shelf life, the design of experiment theory was used. RESULTS: A regression equation in coded values, characterizing the effect of the concentration of the ozone-air mixture, the duration of the sunflower cake treatment and the intensity of the high-frequency field on the sunflower cake shelf life, is obtained. The analysis of the obtained mathematical model of the processing process is performed. CONCLUSION: Experimental studies of the developed line for the production of sunflower cake with quality control of its treatment with an ozone-air mixture have shown that the sunflower cake shelf life depends on the ozone-air mixture concentration and the duration of treatment of the sunflower cake, as well as on the intensity of the high-frequency field. At the same time, with a decrease in the ozone-air mixture concentration, the duration of treatment of the sunflower cake and the intensity of the high-frequency field during the treatment increase. In the area of low concentration, increased duration up to 120 s and intensity up to 15250 V/m, the shelf life of the cake increases. It is reasonable to process sunflower cake with the ozone-air mixture to increase its shelf life from 3 to 5.45 months according to the GOST 80-96 using the developed line (patent RF 2706188) at a concentration of 23.03 mg/m3, processing time of 134 s and a high-frequency field strength of 17374 V/m.

DATA MODELING OF GOLD PRICES USING SUPPORT VECTOR REGRESSION WITH LINEAR, POLYNOMIAL, AND RADIAL BASIS FUNCTION KERNELS

Investment is a commitment of funds or other resources made with the goal of obtaining profits in the future. Gold is one of the commodities favored by investors because of its relatively stable value. Although relatively stable, gold prices experience fluctuations, which introduce risks associated with gold investments. The pattern of gold prices can be mathematically modeled using Support Vector Regression (SVR). SVR finds a function as a hyperplane (separating line) in the form of a regression function that fits all input data with an error and minimizes it as much as possible. SVR enables a balance between data fitting and overfitting through the use of kernel functions. The pattern of gold prices and SVR is the main focus of this research, aiming to model gold prices effectively. Furthermore, SVR seeks to obtain a hyperplane (regression function) that fits all input data by minimizing errors. The gold price modeling results using SVR indicated that the best model was obtained with a linear kernel, showing an error of 0.73% with parameters C = 10^(-4) and ? = 10^(-4). This implies the model's strong ability to follow data patterns accurately, resulting in highly reliable forecasting.

A U-shaped association between composite dietary antioxidant index and migraine in US adults: a nationwide cross-sectional study.

The field of dietary therapies for migraine has grown in popularity. Less research has been conducted to establish the relationship between migraine and the composite dietary antioxidant index (CDAI), a crucial indicator for evaluating the overall combined effects of multiple dietary antioxidants. Therefore, this study addressed this gap based on the National Health and Nutrition Examination Survey (NHANES) database. Multivariate logistic regression equations were used to investigate the relationship between CDAI and migraine, and smoothed-fitted curves were plotted. After a nonlinear relationship was discovered, the recursive algorithm and a two-stage linear regression model were employed to calculate the turning point. Additional stratified analyses were performed to explore differences between populations. This study included a total of 9,190 participants aged 20 years old or older. A U-shaped association was observed between the CDAI and migraine, with an inflection point of 0.2. They were negatively correlated before the inflection point with OR of 0.93 (95% CI = 0.88-0.97) and positively correlated after the inflection point with OR of 1.04 (95% CI = 1.01-1.07). This U-shaped relationship persisted among people aged <60 and ≥60 years, women, and people with BMI <30 and ≥30. We identified a U-shaped association between CDAI and migraine in the U.S. adult population. Further case-control studies and experimental research are needed to explore the underlying mechanisms of action.

Aerobic and anaerobic performance, ability to repeat sprints, and fatigue development during a basketball game-based drill: correlational study

ABSTRACT Fatigue development during basketball matches affects player performance. This study aimed to evaluate the relationship among fatigue development during game-based drills, aerobic and anaerobic performance, and repeated sprint ability (RSA) basketball players. The study included 49 male elite basketball players (23.4 ± 3.8 years, body mass 83.0 ± 8.5 kg, height 189.7 ± 8.9 cm). They performed the Yo-Yo Intermittent Test (YIRT2), RSA test, anaerobic performance assessment (300y; “300-yard shuffle running test”), and a game-based drill. The regression equation for total distance decline during last 3 min of each quarter was TD3 min = −38.11 + 0.253·YIRT2 + 0.276·300y + 0.670·RSA with standard erorr =±4.66 for TD3 min during basketball game-based drill. We found out that RSA performance was the most valuable predictor of TD3 min, explaining 44.89% of variance, 300y explained 10.24%, and YIRT2 7.84%. Notably, 37.03% was unexplained by observed variables. Collectively, RSA is considered an important component of basketball in predicting the delay of neuromuscular fatigue during match but not VO2peak.

Diversity Analysis and Comprehensive Evaluation of 101 Soybean (Glycine max L.) Germplasms Based on Sprout Quality Characteristics.

Soybean sprouts are a common culinary vegetable due to their high nutrition and tasty flavors. To select soybean varieties with excellent sprout quality, 101 soybean materials were collected from different regions of China, and eight sprout quality parameters were determined for overall evaluation. The results showed that eight sprout quality parameters achieved varying degrees of difference and correlation. Based on the principal component analysis (PCA), three principal components were extracted, with a cumulative contribution rate of 78.314%. Further, the comprehensive evaluation value (D) of soybean sprout quality was calculated by membership function analysis based on PCA, and the quality of soybean sprouts was ranked accordingly. Subsequently, a regression equation for the prediction of soybean sprout quality was established using a stepwise regression analysis, and the model showed a good prediction performance (correlation coefficient of prediction > 0.8; residual predictive deviation > 2.0). On these grounds, it was proposed that the quality of soybean sprouts could be comprehensively predicted by four parameters: hypocotyl length, edible rate, 100-seed weight, and total isoflavone content and saponin content. In conclusion, this study provides excellent varieties for soybean sprout production and new variety breeding, and it provides an important reference for the prediction of soybean sprout quality.

Government Expenditure, Human Development Index and Regional Inequality in Indonesia

This study was conducted with the aim of measuring and analyzing the effect of regional government spending on regional inequality through the Human Development Index in Indonesia. This analysis was conducted using the Williamson index as an indicator of regional inequality. This study uses variables of human development spending, infrastructure spending, economic spending, human development index and regional inequality. The research method used is the statistical panel data approach of 34 provinces in Indonesia in 2017-2023 with the Multiple Regression Equation model with AMOS program path analysis. The test results in this study state that directly the variables of human development spending, infrastructure spending, economic spending, and the human development index have a significant effect on regional inequality in Indonesia. Indirectly, the variables of human development spending and economic spending have a significant effect on regional inequality in Indonesia through the human development index, while the variable of infrastructure spending does not affect regional inequality through the human development index.

Forest Aboveground Biomass Estimation Based on Unmanned Aerial Vehicle-Light Detection and Ranging and Machine Learning.

Eucalyptus is a widely planted species in plantation forests because of its outstanding characteristics, such as fast growth rate and high adaptability. Accurate and rapid prediction of Eucalyptus biomass is important for plantation forest management and the prediction of carbon stock in terrestrial ecosystems. In this study, the performance of predictive biomass regression equations and machine learning algorithms, including multivariate linear stepwise regression (MLSR), support vector machine regression (SVR), and k-nearest neighbor (KNN) for constructing a predictive forest AGB model was analyzed and compared at individual tree and stand scales based on forest parameters extracted by Unmanned Aerial Vehicle-Light Detection and Ranging (UAV LiDAR) and variables screened by variable projection importance analysis to select the best prediction method. The results of the study concluded that the prediction model accuracy of the natural transformed regression equations (R2 = 0.873, RMSE = 0.312 t/ha, RRMSE = 0.0091) outperformed that of the machine learning algorithms at the individual tree scale. Among the machine learning models, the SVR prediction model accuracy was the best (R2 = 0.868, RMSE = 7.932 t/ha, RRMSE = 0.231). In this study, UAV-LiDAR-based data had great potential in predicting the AGB of Eucalyptus trees, and the tree height parameter had the strongest correlation with AGB. In summary, the combination of UAV LiDAR data and machine learning algorithms to construct a predictive forest AGB model has high accuracy and provides a solution for carbon stock assessment and forest ecosystem assessment.

Carbonization test and orthogonal polynomial regression analysis of steel fiber reclaimed concrete

To enhance the carbonation resistance of reclaimed concrete, several key factors affecting its performance were investigated. An orthogonal array L16(4³×2⁶) was employed to design the carbonation tests for steel fiber (SF) reinforced concrete. The study included varying SF volume ratios, along with considerations of different concrete ages (T) and water-cement ratios (W/R). The effect of SF volume ratio, regenerated crude aggregate (RCA) replacement rate, W/R, and T on the carbonation resistance of recycled concrete was analyzed. The test results indicated a trend of increasing carbonation depth over time. However, a lower W/R ratio resulted in a reduced carbonation depth. Notably, a 50% RCA replacement rate led to a shallower carbonation depth compared to other replacement rates. After 28 d, recycled concrete containing 1% SF exhibited a carbonation depth that was 6.9%, 1.5%, 1.5%, and 9.3% lower than concrete with 0%, 0.5%, 1.5%, and 2% SF, respectively. Therefore, the incorporation of 1% SF was found to be the most effective in improving carbonation resistance. Orthogonal polynomial regression analysis was employed to develop a regression equation relating carbonation depth to SF volume ratio, RCA replacement rate, W/R, and T. The regression coefficients were calculated and tested, leading to the identification of the optimal regression equation and its corresponding confidence interval.

Prediction of 1cm dose-equivalent rate on the day after administration of 177Lu-DOTATATE from 111In-somatostatine receptor scintigraphy prior to treatment.

When patients administered 177Lu-DOTATATE are released or discharged from rooms where radiopharmaceuticals are used, the time required for release or discharge varies across patients. This study investigated whether the amount of radioactivity accumulated on 111In-somatostatine receptor scintigraphy (111In-SRS) performed prior to treatment can predict the 1cm dose-equivalent rate at a distance of 1m from the patient on the day after 177Lu-DOTATATE administration. Whole-body planar 111In-SRS images were acquired for 21 patients. Pixel values within whole-body and abdominal (35 × 25cm) regions of interest (ROIs) were converted to radioactivity dose (MBq). The 1cm dose-equivalent rate (µSv/h) at a distance of 1m from the patient 18.3 ± 0.5h after administration of 177Lu-DOTATATE was measured using an ionization survey meter. The following relationships were observed between the radioactivity on 111In-SRS and the 1cm dose-equivalent rate on the day after administration of 177Lu-DOTATATE: whole-body ROI: y = 0.16x + 5.01 (r = 0.56, p = 0.009), abdominal ROI: y = 0.27x + 5.13 (r = 0.63, p = 0.002). The regression equations indicate that patients cannot be released or discharged from the radiopharmaceutical room the day after 177Lu-DOTATATE administration if the whole-body and abdominal ROI doses are greater than 81 and 48MBq, respectively, on 111In-SRS. The amount of radioactivity accumulated on 111In-SRS may be a predictor of release criteria for patients receiving 177Lu-DOTATATE.

Estimation of Recovery Efficiency in High‐Temperature Aquifer Thermal Energy Storage Considering Buoyancy Flow

AbstractWith their high storage capacity and energy efficiency as well as the compatibilities with renewable energy sources, high‐temperature aquifer thermal energy storage (HT‐ATES) systems are frequently the target today in the design of temporally and spatially balanced and continuous energy supply systems. The inherent density‐driven buoyancy flow is of greater importance with HT‐ATES, which may lead to a lower thermal recovery efficiency than conventional low‐temperature ATES. In this study, the governing equations for HT‐ATES considering buoyancy flow are nondimensionalized, and four key dimensionless parameters regarding thermal recovery efficiency are determined. Then, using numerical simulations, recovery efficiency for a sweep of the key dimensionless parameters for multiple cycles and storage volumes is examined. Ranges of the key dimensionless parameters for the three displacement regimes, that is, a buoyancy‐dominated regime, a conduction‐dominated regime, and a transition regime, are identified. In the buoyancy‐dominated regime, recovery efficiency is mainly correlated to the ratio between the Rayleigh number and the Peclet number. In the conduction‐dominated regime, recovery efficiency is mainly correlated to the product of a material‐related parameter and the Peclet number. Multivariable regression functions are provided to estimate recovery efficiency using the dimensionless parameters. The recovery efficiency estimated by the regression function shows good agreement with the simulation results. Additionally, well screen designs for optimizing recovery efficiency at various degrees of intensity of buoyancy flow are investigated. The findings of this study can be used for a quick assessment and characterization of the potential HT‐ATES systems based on the geological and operational parameters.

Changing Treatment and Metastatic Disease Patterns in Patients with EGFR Mutated Non-Small Cell Lung Cancer: An ATOMIC Registry Analysis

IntroductionOsimertinib is now a standard 1L therapy for EGFR-mutated advanced non-small cell lung cancer (NSCLC). We aimed to characterize patterns of therapy and longitudinal risk of brain and liver metastasis in a cohort of EGFRm NSCLC. MethodsPatients with metastatic EGFRm NSCLC who received 1L systemic therapy at sites within the Academic Thoracic Medical Investigator’s Consortium (ATOMIC) were included; demographic and clinical data including treatment patterns were described. Analyses of overall survival (OS), time to next treatment (TTNT), and incident brain and liver metastasis were performed on patients who started 1L therapy in ≥2015 using Kaplan-Meier method, Cox regression, and cumulative incidence functions. ResultsThe full cohort included 1,132 patients; mean age 63.4 years, 53% White, 68% female, 67% nonsmoker; 830 patients received 1L systemic therapy in ≥2015. The predominant first EGFR-TKI was erlotinib (65%) prior to 2018 and osimertinib (81%) after 2018. The median TTNT after start of 1L therapy was 13.9 months overall, and longest in patients receiving 1L osimertinib (28 months). In the post 2015 cohort, the baseline prevalence of brain metastasis (BM) was 54% and among patients without baseline brain metastasis, the probability of incident BM at 12, 24, and 48 months was 8%, 22% and 44%, respectively. Development of an on-treatment brain metastasis among patients without baseline brain metastasis was associated with a 3.2 times higher risk of death. ConclusionEven in a contemporary era with prevalent osimertinib use, baseline and longitudinal risk of BM development was high. The ongoing risk of developing BM, together with the associated survival detriment, argues for routine surveillance brain MRIs for patients with EGFRm NSCLC, which are not currently included in guidelines.