Nonlinear Regression Analysis and Its Applications

The paper outlines a method of analysis of intricically non‐linear regression functions. The nonlinear model is first approximated by a cubic spline function. Thereafter, the standard methods of analysis in linear models are applied to obtain estimates and test statistics.

Random norming aids analysis of non-linear regression models with sequential informative dose selection

Questa nota intende dare alcuni criteri generali per costruire stime di parametri da funzioni curve cubiche. Tali funzioni sono particolarmente utili nell'analisi di modelli non lineari per le loro proprieta di convergenza (Ahlberg e altri, 1967). Illustra quindi l'effetto dei coefficienti di correlazione multipla sulle proprieta delle stime quando il modello lineare sottinteso e una funzione esponenziale a tre parametri. Esempi numerici sono gia stati pubblicati dall'Autore (1982, 1984).

<p>Regression analysis is an important statistical tool for analyzing the relationships between dependent, and independent variables. The main goal of regression analysis is determine, and estimate parameters of a function that describe the best fit for a given data sets. There are many linear types of regression analysis models such as simple and multiple regression models. Also, there are the non-linear regression analyses such as binary and multinomial logistic regression models. This research at first, introduced many types of such models. Second, estimates the parameters of the models by using the maximum likelihood estimation, and the least square estimation methods. Also, it introduces some criteria for evaluating methods. Two suitable applications on two different data sets are conducted, and useful results are concluded.</p>

Fuzzy regression based on asymmetric support vector machines

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.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

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.

This study aimed to evaluate the adaptability and phenotypic stability of cowpea genotypes using a nonlinear regression analysis and multivariate analysis. Experiments were performed at four sites in Brazil using a randomized blocks design with 20 treatments and four replications. The adaptability and stability of genotypes were evaluated by Toler nonlinear regression and genotype plus genotype × environment (GGE) biplot methodologies. Most of the genotypes revealed linear response patterns, with no differences regarding the favorable and unfavorable environments. Regarding the genotype classification for stability and adaptability, the Toler and GGE biplot methodologies are congruent. Genotypes MNC99-537F-4, MNC00-561G-6, MNC99542F-5, and Patativa have high overall adaptability and adequate yield. Therefore, they should be recommended for cultivation in the tested environments. Genotypes closer to the ideotype by the GGE biplot method are considered doubly desirable by the nonlinear method.

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.

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.

Evaluation of one-dimensional freezing behavior for ice-rich sandy soil

Modeling of resistance spot welding process on galvanized steel sheet was investigated. Mathematical models developed by nonlinear multiple regression analysis and artificial neural network approach were employed in the prediction of welding quality factors, namely nugget diameter, penetration rate and tensile shear strength, under some welding conditions. According to the prediction models on quality, the prediction systems of welding process parameters were formulated respectively on the basis of Newton-Raphson iterative algorithm and cascade forward back propagation algorithm in order to obtain the desired welding quality. The results showed that the prediction precision of cascade forward back propagation algorithm was higher than Newton-Raphson iterative algorithm. The current duration had the largest prediction error, followed by electrode force and welding current. Therefore, it was concluded that the current duration was the most difficult parameter in prediction system of welding process in order to obtain the desired welding quality.

Advanced driver assistance systems have been an active research topic for decades, for which many approaches have been developed not only to reduce the number of traffic accidents but also to increase the driver’s comfort. Among the many different solutions proposed, learning-based prediction approaches have gained considerable attention in recent years. Within this scope, this work focuses on the implementation aspects of a linear learning-based regression model for detecting unintended lane-departures, where the goal is to achieve a prediction model with good predictive performance while keeping the computational complexity as low as possible. Aspects under consideration include input signal selection and down-sampling. The linear prediction model is analyzed using a real world data set, and benchmarked against a kinematic constant velocity model and a non-linear regression model. The results show that the linear regression model has a significantly higher prediction performance when compared to a kinematic model. It is also shown that the predictive performance remains comparable to the more complex nonlinear regression model, even though the computational complexity of the linear model is significantly lower.

Fixed-bed column dynamics of tetracycline hydrochloride using commercial grade activated carbon: comparison of linear and nonlinear mathematical modeling studies