Non-Linear and Smooth Regression

Numerous studies have tested the relationship between vegetation density (using normalized difference vegetation index/NDVI as a proxy for vegetation density) and land surface temperature (LST) using a linear regression model. Few studies have explicitly compared linear and nonlinear regression models in describing the relationship between NDVI and LST in different intensities of anthropogenic activities. Hence, this study aims to investigate multitemporal variations of LST and to compare the performance of NDVI as a proxy for LST over various urban activities in Yogyakarta City, Indonesia. NDVI and LST were extracted from Landsat images for 2019, 2020, 2021, and 2022. The years of 2019, 2020, 2021, and 2022 represent different anthropogenic activities i.e. pre Covid-19, emergency response to Covid-19, transition period of Covid-19, and new normal conditions, respectively. The mean LST of 2019, 2020, 2021, and 2022 were 29.64 °C, 24.52 °C, 28.93 °C, and 29.47 °C, respectively, in which the lowest temperature was during emergency response to Covid-19. During emergency response to Covid-19 in 2020, the highest R2 was non-linear logarithmic regression by 0.31, while the highest R2 for 2019, 2021, and 2022 was R2 of nonlinear exponential regression by 0.36, 0.45, and 0.56, respectively. However, linear regression models were still relatively good at describing the relationship between NDVI and LST during the whole period by having R2 of 0.30 to 0.55.

Fuzzy regression based on asymmetric support vector machines

Research on the non-smooth problems in the nonlinear support vector regression. A nonlinear smooth support vector regression model is proposed. Using a generalized cubic spline function approach the non-smooth part in the support vector regression model. The model of the nonlinear smooth support vector regression is solved by BFGS-Armijo. Then, the approximation accuracy and the astringency of the generalized cubic spline function to the insensitive loss function were analyzed. As a result, we found the four-order and six times spline function's approximation effect is better than other smooth functions, and the nonlinear smooth support vector regression model, which be proposed in this paper is convergent.

In this paper, heteroscedastic nonlinear regression (HNLR) models under the flexible class of two–piece distributions based on the scale mixtures of normal (TP–SMN) family were examined. This novel class of nonlinear regression (NLR) models is a generalization of the well-known heteroscedastic symmetrical nonlinear regression models. The TP–SMN is a rich class of distributions that covers symmetric and asymmetric as well as heavy-tailed distributions. Using the suitable hierarchical representation of the family, the researchers first derived an EM–type algorithm for iteratively computing maximum likelihood (ML) estimates of the parameters. Then, in order to examine the performance of the proposed models and methods, some simulation studies were presented to show the robust aspect of this flexible class against outlying and also atypical data. As the last step, a natural real dataset was fitted under the proposed HNLR models.

BackgroundThe most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited.MethodsColony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis.ResultsBoth the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed the extraction of scores of radioresistance, which displayed significant correlations with the estimated parameters of the regression models.ConclusionsUndoubtedly, LQ regression is a robust method for the analysis of clonogenic survival data. Nevertheless, alternative approaches including non-linear regression and multivariate techniques such as cluster analysis and principal component analysis represent versatile tools for the extraction of parameters and/or scores of the cellular response towards ionizing irradiation with a more intuitive biological interpretation. The latter are highly informative for correlation analyses with other types of data, including functional genomics data that are increasingly beinggenerated.

The adaptive neuro-fuzzy inference system (Anfis) is considered for flow over rectangular side weirs located on a straight channel as a substantial part of distribution channels in irrigation systems and treatment units. To estimate the outflow over a rectangular sharp-crested side weir, the discharge coefficient in the side weir equation needs to be determined in accordance with the effective dimensionless parameters F1 (Froude number), L/b (weir length/channel width), L/h1 (weir length/flow depth), and p/h1 (weir height/flow depth). The discharge coefficient of rectangular side weirs was determined using 843 laboratory test results. The performance of the Anfis model is compared with multilinear and nonlinear regression models. The criteria used for the evaluation of the performance of models are root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics. Comparison results indicated that the Anfis technique could be successfully employed in modelling discharge coefficients. It is found that the Anfis model with RMSE of 0·043 in the test period is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0·054 and 0·106, respectively.

این مطالعه به منظور بررسی پیش بینی شاخص های عملکرد تولیدی در مرغان تخم گذار با استفاده از شبکه های عصبی مصنوعی و رگرسیون غیرخطی چندگانه انجام شد. بررسی بر روی اطلاعات چهار دوره متوالی پرورش در یک واحد پرورش مرغ تخم گذار صورت گرفت. روش های داده-کاوی شامل رگرسیون خطی و غیر خطی، شبکه عصبی پرسپترون سه لایه، شبکه عصبی پرسپترون چهار لایه و شبکه عصبی با تابع پایه ای شعاعی بود. در این مدل ها از متغیرهای سن گله، میزان خوراک مصرفی و فصل تولید به عنوان متغیر پیشگو و شاخص های عملکرد تولیدی شامل درصد تخم-گذاری، وزن توده ای تخم مرغ تولیدی و ضریب تبدیل غذایی به عنوان متغیر پاسخ استفاده شد. نتایج نهایی رگرسیون های خطی نشان داد که برای تمامی متغیرهای وابسته مورد مطالعه متغیر مستقل سن گله معنی دار می باشد. بنابراین رگرسیون غیر خطی شاخص های عملکرد تولیدی در مقابل سن برای مقایسه با شبکه های عصبی مختلف مورد بررسی قرار گرفت و برای مقایسه کلیه مدل ها از ضریب تعیین (R2) و میانگین قدر مطلق خطا (MAE) استفاده شد. نتایج نشان داد بین شبکه های عصبی مصنوعی مختلف مورد مطالعه، شبکه با تابع پایه ای شعاعی بهتر از سایر مدل های در پیش‌بینی شاخص های عملکرد تولیدی مرغان تخم گذار عمل می کند.

First of all, aiming at studying the relationship between ethanol conversion, C4 olefin selectivity and temperature for each catalyst using the knowledge of fitting arbitrary data and adopting the basic idea of control variable method, linear regression equation and nonlinear regression equation model are established. Aiming at the solution of linear regression and non-linear regression model, this paper uses the fitting algorithm to calculate the functional relationship between the two variables, and uses Matlab to solve the specific function expression and draw the function relation diagram to further solve the relationship between catalyst combination, temperature and ethanol conversion and C4 olefin selectivity.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Water is considered as an essential commodity in human society. It has been observed that the basic standard of living of any Country can be measure through the effective portable water supply for consumption, sanitation and hygiene for the citizen. Its production and supply in the Federal Capital Territory (FCT), Abuja, Nigeria is a challenge, as dominant percentages of lower- class workforce live outside the FCTWB existing water network, and depend on borehole or tanker for water. The demand on the water supply system in FCT, Abuja has exceeded its initial design population, and the system is incomplete and operating with only 720 million liter of water per day (MLD) functioning plant. On this basis, this study seeks to identify the best model that fit daily water supply data in FCT, Abuja and to forecast the future daily water supply in this area. The comparing models were artificial neural, multiple linear and non-linear regression model were applied to the data set of daily water production, daily water treated, daily water supply, daily water leakage, Number of household connected to Federal Capital Territory Water board water network, Number of Commercial area connected to Federal Capital Territory Water board water network, and the Estimated population of Federal Capital Territory ,Abuja from (2013 to 2020), and it was emerged that the most adequate model for the data was Multiple linear regression model (MLR), with (R2 =1.000), (RMSE = 0.00282), and (MAE = 6.540). Artificial neural network records the high value of (RMSE = 432.4321), (MAE = 549.444) and (R2 =0.921), and multiple nonlinear regression record the highest value of (RMSE = 806.687), (MAE = 666.421) and (R2 = 0.999). From the statistical measure of goodness of fit, the three models compared results indicate that MLR model forecast are closely matching with actual observations values, artificial neural network model over-forecast some days volume of daily water supply by FCTWB, cooperation and multiple nonlinear regression model under-forecast some days volume of daily water supply by FCTWB, corporation. The three models compared depicts the influential variables of FCTWB Corporation daily water supply, (ANN = DWP, DWT), (MLR = DWT, DWL) and (MNLR = DWP, DWL), and their forecast graphs shows downward daily water supply in FCT, Abuja. It is recommended that the FCT, Abuja water Board Corporation should consider multiple linear regression (MLR) model and its forecasted values as a road map in its operations and planning toward water supply sustainability in FCT, Abuja.

Ozone forecast models using nonlinear regression (NLR) have been successfully applied to daily ozone forecast for seven metro areas in Kentucky, including Ashland, Bowling Green, Covington, Lexington, Louisville, Owensboro, and Paducah. In this study, the updated 2005 NLR ozone forecast models for these metro areas were evaluated on both the calibration data sets and independent data sets. These NLR ozone forecast models explained at least 72% of the variance of the daily peak ozone. Using the models to predict the ozone concentrations during the 2005 ozone season, the metro area mean absolute errors (MAEs) of the model hindcasts ranged from 5.90 ppb to 7.20 ppb. For the model raw forecasts, the metro area MAEs ranged from 7.90 ppb to 9.80 ppb. Based on previously developed NLR ozone forecast models for those areas, Takagi-Sugeno fuzzy system models were developed for the seven metro areas. The fuzzy "c-means" clustering technique coupled with an optimal output predefuzzification approach (least square method) was used to train the Takagi-Sugeno fuzzy system. Two types of fuzzy models, basic fuzzy and NLR-fuzzy system models, were developed. The basic fuzzy and NLR-fuzzy models exhibited essentially equivalent performance to the existing NLR models on 2004 ozone season hindcasts and forecasts. Both types of fuzzy models had, on average, slightly lower metro area averaged MAEs than the NLR models. Among the seven Kentucky metro areas Ashland, Covington, and Louisville are currently designated nonattainment areas for both ground level O 3 and PM 2.5 . In this study, summer PM 2.5 forecast models were developed for providing daily average PM 2.5 forecasts for the seven metro areas. The performance of the PM 2.5 forecast models was generally not as good as that of the ozone forecast models. For the summer 2004 model hindcasts, the metro-area average MAE was 5.33ìg/m 3 . Exploratory research was conducted to find the relationship between the winter PM 2.5 concentrations and the meteorological parameters and other derived prediction parameters. Winter PM 2.5 forecast models were developed for seven selected metro areas in Kentucky. For the model fits, the MAE for the seven forecast models ranged from 3.23 ìg/m 3 to 4.61 ìg/m 3 (~26-28% NMAE). The fuzzy technique was also applied on PM 2.5 forecast models to seek more accurate PM 2.5 prediction. The NLR-fuzzy PM 2.5 had slightly better performance than the NLR models.

Criteria for global minimum of sum of squares in nonlinear regression

Wiley-Interscience Paperback Series Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models ...highly recommend[ed] ...for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression -Technometrics [This book] provides a good balance of relevant theory and application with many examples ...[and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students. -Mathematical Reviews [This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition ...[and is] a worthwhile reference for the marketing researcher with a serious interest in linear models. -Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. book also includes pseudocode for computing algorithms.

The novel coronavirus COVID-19 originally identified in December 2019, based on the data issued by March 30, 2020 daily report, the epidemic of SARS-CoV-2 so far has caused 693224 cases and resulted in 33106 deaths in more than 200 countries. Referring to the data reported, World Health Organization declared the outbreak a pandemic. Several Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2 or COVID-19), showed high transmission capacity and morbidity. In this way, WHO suggests that the most efficient method for controlling transmission is social isolation/quarantine to the population. New cases of the pandemic arose everyday but Nigeria recorded its first death in 23rd March, 2020. The study used a secondary data culled from Worldometer from March 23, 2020 – May 5, 2020. The study examined the polynomial relationship between day and new cases of coronavirus in Nigeria and also check whether new cases will be predicted. Though, linear regression model was fitted to check the model that best fit the data. Result showedthat days had a positive effect on new cases and was found significant at P-value < 0.01 (1% significance level) for both linear and non-linear regression model. It was also revealed that nonlinear regression model best fit the model with an improved adjusted R square. It was established that there is a statistically significant relationship between days and new cases.However, government should take proper measures to reduce the spread of coronavirus and law enforcement the measures should be put into consideration. Keywords: Coronavirus, relationship, New cases, New death, Model DOI: 10.7176/RHSS/12-9-02 Publication date: May 31 st 2022

Research on nonlinear prediction model of weld forming quality during hot-wire laser welding