Linear Regression Function Research Articles

Impact of rising temperatures on historical wheat yield, phenology, and grain size in Catalonia.

Climate change poses significant challenges to agriculture, impacting crop yields and necessitating adaptive strategies in breeding programs. This study investigates the genetic yield progress of wheat varieties in Catalonia, Spain, from 2007 to 2021, and examines the relationship between genetic yield and climate-related factors, such as temperature. Understanding these dynamics is crucial for ensuring the resilience of wheat crops in the face of changing environmental conditions. Genetic yield progress was assessed using a linear regression function, comparing the average yield changes of newly released wheat varieties to benchmark varieties. Additionally, a quadratic function was employed to model genetic yield progress in winter wheat (WW). The study also analyzed correlations between genetic yield (GY) and normalized values of hectoliter weight (HLW) and the number of grains (NG) for both spring wheat (SW) and WW. Weather data were used to confirm climate change impacts on temperature and its effects on wheat growth and development. The study found that genetic yield was stagnant for SW but increased linearly by 1.31% per year for WW. However, the quadratic function indicated a possible plateau in WW genetic yield progress in recent years. Positive correlations were observed between GY and normalized values of HLW and NG for both SW and WW. Climate change was evident in Catalonia, with temperatures increasing at a rate of 0.050 °C per year. This rise in temperature had detrimental effects on days to heading (DH) and HLW, with reductions observed in both SW and WW for each °C increase in annual minimum and average temperature. The findings highlighted the urgent need to address the impact of climate change on wheat cultivation. The stagnation of genetic yield in SW and the potential plateau in WW genetic yield progress call for adaptive measures. Breeding programs should prioritize phenological adjustments, particularly sowing date optimization, to align with the most favorable months of the year. Moreover, efforts should be made to enhance HLW and the number of grains per unit area in new wheat varieties to counteract the negative effects of rising temperatures. This research underscores the importance of ongoing monitoring and adaptation in agricultural practices to ensure yield resilience in the context of a changing climate.

Pattern of Agricultural Progress in India’s North-East and the Contributing Factors: An Econometric Analysis

Despite being blessed with rich agro-climatic conditions, the largest agrarian state in India’s North-East, Assam recorded relatively poor agricultural growth, since independence. The question of agricultural performance in terms of use of factors and growth pattern always arise that seems to vary in different stages of policy shift. Agricultural diversity increased in the initial phase with the expansion of agricultural area but slowed down in the later stages. However, the nature of agricultural diversity and use of resources including land allocations reflects the adaptation of farming community, absorption of labour force and sustainability of earning of farmers. The objectives are to analyze: i) the pattern of agricultural growth, diversity; ii) relative contribution of crop diversification, yield and area towards output growth in the pre-Green Revolution, Green Revolution and Post-Reform period; iii) association of various factors with crop yields in the short run and the adjustment process in the long run. Using secondary data, semi-log linear and spline regression functions we examined the growth and stationarity of growth processes is checked by ADF test. Times series analyses like cointegration and ARDL bound testing approach has been followed to examine the relation of various factors with yield of various crops in the short and long run. The ECM also provides the process of adjustment and CUSUM(Q) test is used for checking fitness of the models. Changes in diversity are analyzed through Herfindahl Index and the additive decomposition technique is employed to examine changing contribution of growth of yield, area and cropping pattern and their interactions. The result reveals varied impacts of main weather variable (rainfall), technological factors and cropping intensity on the yields of crops in different phases since 1950-51. Area effect on output and cropping pattern growth though declined, yield growth contributed increasingly in successive sub-periods in Assam. However, the contribution of modern technology towards the growth has not been uniform in the three major stages of agricultural transformation in Assam.

On the validity of the bootstrap hypothesis testing in functional linear regression

On the validity of the bootstrap hypothesis testing in functional linear regression

The guarantees of origin as a market-based energy transition mechanism in Poland

A transition from generating electricity from conventional sources to generating it from renewables is one of drivers leading us towards a circular economy. Electricity is a specific product and regardless of where and how it is produced, it takes the same form. A novel aspect of the research is the examination of correlations and relationships between guarantees of origin. The research objective is to analyse the market for the guarantees of origin in the volatile price environment that we had late 2021 and early 2022. Therefore, we analysed demand for the guarantees in January 1, 2020 to June 30, 2022 and the correlation between the price of electricity and guarantees of origin. It was based on the secondary data analysis method and the use of Pearson’s correlation coefficient and a linear regression function. The authors of the study made a hypothesis that the trading volume would increase during the study period and that there would be a positive correlation between the price of energy and the guarantees of origin. A key finding of the study revealed a steady increase in the purchase of guarantees despite the rise in prices. The buying of the guarantees is not a top-down requirement, but rather a bottom-up action, which indicates growing social expectations towards enterprises to consume energy from renewable sources.

Robust estimations of areal grain size distribution from geometric surface roughness in a proglacial outwash area

Rapid glacier mass loss in high-alpine catchments exposes unconsolidated sediments to erosion by meltwater-fed mountain streams, with impact on the catchment-scale sediment dynamics. Proglacial outwash areas (OWA) are a key spatial element in this sediment flux cascade, with grain size distributions (GSD) as an integral variable in current and future glacio-fluvial processes and associated effects.In this study, surface grain size estimation methods based on linear correlations between geometric surface roughness and GSD data are adapted to test this new mapping approach for areal GSD patterns and their changes in a proglacial OWA. Surface roughness is computed with adaptive kernel sizes from high-resolution topographic point clouds derived from UAV-based photogrammetry. For model calibration, ground truth data is manually obtained from 30 dry-exposed GSD sampling patches of 1 m2 each. The novelty and potential of this surface roughness regression model lies in its capability to robustly map GSD percentiles at 1-m cell resolution in highly dynamic proglacial environments and inherent data scarcity, drastically reducing the portion of labour-intensive and time-consuming manual surveying.Our optimized linear regression function for the key figure D84, which is widely used in practice, returns a coefficient of determination of 76.4 %. The linear relation found between the D84 of field GSD and the 84th distribution percentile of surface roughness metrics has a slope of α = 6.01, which is consistent with the range of recently published studies using LiDAR-based and photogrammetric surveys. The presented surface roughness regression model provides realistic surficial estimations of areal GSD patterns in a proglacial domain of sediment remobilization. In addition, this work analyses and discusses detected changes in the estimated D84 over a three-month period. A systematic shift is identified for sediment compositions with an initial D84 above 60 mm. This is thought to be an effect of the original image quality and variable lighting conditions between photogrammetric surveys and indicates that best practice should include careful survey planning for most uniform flight settings. Nevertheless, visually verified significant changes in D84 along frequently wet low-flow channels can be detected automatically, and thus the findings demonstrate the feasibility of this GSD monitoring approach for tracking fluvial re-working of surface sediment.

Analysis of bridge displacement using GNSS time-series data

Analysis and identifying the displacement characteristics play a key role in timely monitoring and detecting the physical responses of the bridge to ensure the safety of the human and structure. Many previous kinds of research used GNSS data to identify displacement and oscillation modelling of the bridge with different algorithms. This study uses GNSS time-series data to determine linear displacement and model oscillation of the bridge using a procedure including filtering outliers, linear regression, and sin function to identify amplitude in three directions, the plane displacement velocity, spatial displacement velocity, and vibration model of the bridge. The data in the research in the GNSS time-series data from three P5 GNSS receivers of the CHC brand on the Dachongyong bridge in Nanning, China with 1646 observations, at one-hour sample intervals in 68 consecutive days. The plane and spatial velocity of the three points DCQ01, DCQ02, and DCQ03 is 0.0181 mm/h, 0.0185 mm/h; 0.0114 mm/h, 0.0173 mm/h; and 0.0071 mm/h, 0.0082 mm/h respectively. The study results are significant in analyzing and identifying the bridge’s displacement characteristics.

Computational reactive–diffusive modeling for stratification and prognosis determination of patients with breast cancer receiving Olaparib

Mathematical models based on partial differential equations (PDEs) can be exploited to handle clinical data with space/time dimensions, e.g. tumor growth challenged by neoadjuvant therapy. A model based on simplified assessment of tumor malignancy and pharmacodynamics efficiency was exercised to discover new metrics of patient prognosis in the OLTRE trial. We tested in a 17-patients cohort affected by early-stage triple negative breast cancer (TNBC) treated with 3 weeks of olaparib, the capability of a PDEs-based reactive–diffusive model of tumor growth to efficiently predict the response to olaparib in terms of SUVmax detected at 18FDG-PET/CT scan, by using specific terms to characterize tumor diffusion and proliferation. Computations were performed with COMSOL Multiphysics. Driving parameters governing the mathematical model were selected with Pearson's correlations. Discrepancies between actual and computed SUVmax values were assessed with Student’s t test and Wilcoxon rank sum test. The correlation between post-olaparib true and computed SUVmax was assessed with Pearson’s r and Spearman’s rho. After defining the proper mathematical assumptions, the nominal drug efficiency (εPD) and tumor malignancy (rc) were computationally evaluated. The former parameter reflected the activity of olaparib on the tumor, while the latter represented the growth rate of metabolic activity as detected by SUVmax. εPD was found to be directly dependent on basal tumor-infiltrating lymphocytes (TILs) and Ki67% and was detectable through proper linear regression functions according to TILs values, while rc was represented by the baseline Ki67-to-TILs ratio. Predicted post-olaparib SUV*max did not significantly differ from original post-olaparib SUVmax in the overall, gBRCA-mutant and gBRCA-wild-type subpopulations (p > 0.05 in all cases), showing strong positive correlation (r = 0.9 and rho = 0.9, p < 0.0001 both). A model of simplified tumor dynamics was exercised to effectively produce an upfront prediction of efficacy of 3-week neoadjuvant olaparib in terms of SUVmax. Prospective evaluation in independent cohorts and correlation of these outcomes with more recognized efficacy endpoints is now warranted for model confirmation and tailoring of escalated/de-escalated therapeutic strategies for early-TNBC patients.

Research and analysis on the preparation of C4 olefin by ethanol coupling method based on regression algorithm with computer technology

Computer technology has been used to study the different combination of catalyst and temperature on the ethanol conversion (one-way conversion rate of 100% per unit time ethanol (alcohol intake - ethanol residue)/ethanol intake) and C4 olefin selectivity (the proportion of all products of C4 olefin), it is necessary to decompose the catalyst composition into several indicators. The effects of several indexes on ethanol conversion and C4 olefins selectivity were analyzed by computer technology. Canonical correlation analysis was used to study them, and the coefficient before each component represented the degree of importance. The results showed that the higher the catalyst combination temperature, the higher the weight of hydroxyapatite, the higher the ethanol conversion and C4 olefins selectivity, and vice versa. When the C4 olefin yield (its value is the selectivity of C4 olefin to ethanol conversion) is as high as possible, the multiple linear stepwise regression function of catalyst parameters and temperature on C4 olefin yield is obtained. MATLAB software was used to calculate the function formula. The absolute value of coefficients determines the importance of each index to C4 olefin yield. Combined with chemical reaction, when the mass ratio is 200:200 and the temperature is 400℃, the yield of C4 olefins can be maximized, and the yield of C4 olefins is 44.728%. Through the establishment of decision tree regression model by computer technology, it can be intuitively concluded that when the temperature is lower than 350℃, the best experimental condition is the C4 olefins yield of 17.264%.

Correction: CLT in functional linear regression models

Correction: CLT in functional linear regression models

Robust estimation for functional quadratic regression models

Functional quadratic regression models postulate a polynomial relationship rather than a linear one between a scalar response and a functional covariate. As in functional linear regression, vertical and especially high–leverage outliers may affect the classical estimators. For that reason, providing reliable estimators in such situations is an important issue. Taking into account that the functional polynomial model is equivalent to a regression model that is a polynomial of the same order in the functional principal component scores of the predictor processes, our proposal combines robust estimators of the principal directions with robust regression estimators based on a bounded loss function and a preliminary residual scale estimator. Fisher–consistency of the proposed method is derived under mild assumptions. Consistency, asymptotic robustness as well as an expression for the influence function of the related functionals are derived when the covariates have a finite–dimensional expansion. The results of a numerical study show the benefits of the robust proposal over the one based on sample principal directions and least squares for the considered contaminating scenarios. The usefulness of the proposed approach is also illustrated through the analysis of a real data set which reveals that when the potential outliers are removed the classical method behaves very similarly to the robust one computed with all the data.

Variable Selection in Multivariate Functional Linear Regression

Variable Selection in Multivariate Functional Linear Regression

Prediction of nitrate concentrations using multiple linear regression and radial basis function neural network in the Cheliff River basin, Algeria

In this paper, multiple linear regression (MLR) and radial basis function neural network (RBF-NN) are applied to predict nitrate (NO3 -) concentration with and without reservoir volume (WV) as predictor using monthly data for ten years in three water reservoirs located in the upper Cheliff basin (NW of Algeria). The datasets were divided into training (80%) and testing (20%) sets and two different scenarios were compared. The results revealed that RBF-NN was more efficient (MAE = 0.192 and SI = 0.061) compared with the MLR model to predict NO3 - in all reservoirs. RBF-NN provided the best accuracy in the testing period with a high R2 of 0.957 in reservoir II, and low MSE and PBias of 0.048 mg/l and 2.98% in the training period in reservoir III, respectively. Overall, the best results were generated by M(iii) in scenario B.

Modelling an automated rainfall forecasting system using an optimized intelligent agent

Weather forecasting information is very crucial in decision making process regarding to activities and works, such as in the field of agriculture to determine initial growing season. Recently, climate change causes trouble in weather forecasting. Time series data analysis for forecasting, is one of the most important aspects of the practical usage. Time Series data is large in volume, highly dimensional and continuous updating. Accurate rainfall forecasting with the help of time series data analysis had helped in the field of agriculture, in evaluating drought and flooding situations in advance. The data used within this paper is taken from Automatic Digital Meteorological Station (NECOP Station) in National Space Research and Development Agency (NASRDA-Centre for Basic Space Science, Nsukka, Enugu State Nigeria). Those data include ambient temperature, air pressure, solar radiation, relative humidity, and wind speed etc. In this paper, rainfall forecasting models were developed for Artificial Neural Network (ANN) based on Levenberg-Marquardt training function and Multiple linear regression (MLR) and was used for the prediction. Based on experimental result, it was concluded that prediction using ANN model for NASRDA-CBSS weather data produced prediction with more than 90% accuracy while MLR prediction gives 70%.

Strategies for constructing mathematical models of nonlinear systems based on multiple linear regression models

Abstract Mathematical systems often have nonlinear, time-varying, time-lagged, and uncertain factors, which affect the experimental prediction accuracy. In order to improve the experimental prediction accuracy, this paper inputs the independent and dependent variable data sets as the original samples into a multiple linear regression function performs fitting calculations to obtain the nonlinear factors, and constructs a mathematical model of nonlinear systems based on a multiple linear regression model. In this model, the expected output value is calculated, and the input vector and output vector are continuously controlled for rolling operations to obtain the prediction results. A mathematical experiment of nonlinear system dynamics of vibration of deep water trap-test pipe system is set up to test the prediction ability of the model. The results show that the nonlinear system mathematical model based on the multiple linear regression model has a very high prediction accuracy. In the mathematical experiments of vibration nonlinear system dynamics of deep water trap-test pipe system, the error of the nonlinear system mathematical model based on multiple linear regression model in the transverse flow vibration frequency of the trap pipe column is 2%, which is lower than the single trap pipe calculation model by 4%. The prediction accuracy of the nonlinear system mathematical model based on the multiple linear regression model is higher than that of the single test tube model calculation by 78%. This shows that the nonlinear system mathematical model based on the multiple linear regression model can improve the experimental prediction accuracy.

Predicting the Activity of Oral Lichen Planus with Glycolysis-related Molecules: A Scikit-learn-based Function.

Oral lichen planus (OLP) is one of the most common oral mucosa diseases, and is mainly mediated by T lymphocytes. The metabolic reprogramming of activated T cells has been shown to transform from oxidative phosphorylation to aerobic glycolysis. The present study investigated the serum levels of glycolysis-related molecules (lactate dehydrogenase, LDH; pyruvic acid, PA; lactic acid, LAC) in OLP, and the correlation with OLP activity was assessed using the reticular, atrophic and erosive lesion (RAE) scoring system. Univariate and multivariate linear regression functions based on scikit-learn were designed to predict the RAE scores in OLP patients, and the performance of these two machine learning functions was compared. The results revealed that the serum levels of PA and LAC were upregulated in erosive OLP (EOLP) patients, when compared to healthy volunteers. Furthermore, the LDH and LAC levels were significantly higher in the EOLP group than in the nonerosive OLP (NEOLP) group. All glycolysis-related molecules were positively correlated to the RAE scores. Among these, LAC had a strong correlation. The univariate function that involved the LAC level and the multivariate function that involved all glycolysis-related molecules presented comparable prediction accuracy and stability, but the latter was more time-consuming. It can be concluded that the serum LAC level can be a user-friendly biomarker to monitor the OLP activity, based on the univariate function developed in the present study. The intervention of the glycolytic pathway may provide a potential therapeutic strategy.

Gene-level association analysis of bivariate ordinal traits with functional regressions.

In genetic studies, many phenotypes have multiple naturally ordered discrete values. The phenotypes can be correlated with each other. If multiple correlated ordinal traits are analyzed simultaneously, the power of analysis may increase significantly while the false positives can be controlled well. In this study, we propose bivariate functional ordinal linear regression (BFOLR) models using latent regressions with cumulative logit link or probit link to perform a gene-based analysis for bivariate ordinal traits and sequencing data. In the proposed BFOLR models, genetic variant data are viewed as stochastic functions of physical positions, and the genetic effects are treated as a function of physical positions. The BFOLR models take the correlation of the two ordinal traits into account via latent variables. The BFOLR models are built upon functional data analysis which can be revised to analyze the bivariate ordinal traits and high-dimension genetic data. The methods are flexible and can analyze three types of genetic data: (1) rare variants only, (2) common variants only, and (3) a combination of rare and common variants. Extensive simulation studies show that the likelihood ratio tests of the BFOLR models control type I errors well and have good power performance. The BFOLR models are applied to analyze Age-Related Eye Disease Studydata, in which two genes, CFH and ARMS2, are found to strongly associate with eye drusen size, drusen area, age-related macular degeneration (AMD) categories, and AMD severity scale.

Partially functional linear quantile regression model and variable selection with censoring indicators MAR

In this paper, we study the quantile regression (QR) estimation for the partially functional linear model with the responses being right-censored and the censoring indicators being missing at random (MAR). Firstly, we construct the weighted QR estimators for both the infinite-dimensional slope function and the finite scalar parameters of the model by combining the methods of calibration, imputation and inverse probability weighting. Then, some asymptotic properties such as the convergence rate of the estimator for the slope function and the asymptotic distribution of the estimator for the finite scalar parameters are obtained respectively. Moreover, to select the scalar covariates in the model, we also give a variable selection procedure by the method of adaptive LASSO penalty and establish the oracle property of the proposed weighted penalized estimators simultaneously. Finally, some simulation studies and a real data analysis are carried out to show the performances of the proposed methods.

Gene Association Analysis of Quantitative Trait Based on Functional Linear Regression Model with Local Sparse Estimator.

Functional linear regression models have been widely used in the gene association analysis of complex traits. These models retain all the genetic information in the data and take full advantage of spatial information in genetic variation data, which leads to brilliant detection power. However, the significant association signals identified by the high-power methods are not all the real causal SNPs, because it is easy to regard noise information as significant association signals, leading to a false association. In this paper, a method based on the sparse functional data association test (SFDAT) of gene region association analysis is developed based on a functional linear regression model with local sparse estimation. The evaluation indicators CSR and DL are defined to evaluate the feasibility and performance of the proposed method with other indicators. Simulation studies show that: (1) SFDAT performs well under both linkage equilibrium and linkage disequilibrium simulation; (2) SFDAT performs successfully for gene regions (including common variants, low-frequency variants, rare variants and mix variants); (3) With power and type I error rates comparable to OLS and Smooth, SFDAT has a better ability to handle the zero regions. The Oryza sativa data set is analyzed by SFDAT. It is shown that SFDAT can better perform gene association analysis and eliminate the false positive of gene localization. This study showed that SFDAT can lower the interference caused by noise while maintaining high power. SFDAT provides a new method for the association analysis between gene regions and phenotypic quantitative traits.

Literacy achievement between women and men according to the Program for the International Assessment of Adult Competencies

The literacy of a country is key to the development of society. This work aims to find out if there are differences between the reading abilities of men and women between the ages of 16 and 24 compared to other older age groups, and if this behavior is consistent among the 22 countries that carried out the Program for the International Assessment of Adult Competencies test. The intsvy library was used in the R and RStudio software, and the linear regression function. The results do not show significant differences between the scores of men and women. However, there are significant differences between different age groups and countries. People between the ages of 25 and 34 tend to have higher literacy scores than the rest of the countries.

A multi-model study for understanding the contamination mechanisms, toxicity and health risks of hardness, sulfate, and nitrate in natural water resources.

Several water quality contaminants have attracted the attention of numerous researchers globally, in recent times. Although the toxicity and health risk assessments of sulfate and water hardness have not received obvious attention, nitrate contamination has gained peculiar research interest globally. In the present paper, multiple data-driven indexical, graphical, and soft computational models were integrated for a detailed assessment and predictive modeling of the contamination mechanisms, toxicity, and human health risks of natural waters in Southeast Nigeria. Majority of the tested physicochemical parameters were within their satisfactory limits for drinking and other purposes. However, total hardness (TH), SO4, and NO3 were above stipulated limits in some locations. A nitrate health risk assessment revealed that certain areas present a chronic health risk to children, females, and males due to water intake. However, the dermal absorption route was found to have negligible health risks. SO4 in some locations was above the 100mg/L Nigerian limit; thus, heightening the potentialhealth effects due to intake of the contaminatedwater resources. Most samples had low TH values, which exposes users to health defects. There are mixed contamination mechanisms in the area, according to graphical plots, R-mode hierarchical dendrogram, factor analysis, and stoichiometry. However, geogenic mechanisms predominate over human-related mechanisms. Based on the results, a composite diagrammatic model was developed. Furthermore, predictive radial basis function (RBF) and multiple linear regression (MLR) models accurately predicted the TH, SO4, and NO3, with the RBF outperforming the MLR models. Insights from the RBF and MLR models were useful in validating the results of the hierarchical dendrogram, factor, stoichiometric, and graphical analyses.