Non-Linear Regression Forecast Model and Learning Algorithm Based on Functional Networks

2010 ◽  
Vol 159 ◽  
pp. 595-598
Author(s):  
Xiang Hu Liu
Keyword(s):  
Linear Regression ◽  
Linear Model ◽  
Traditional Method ◽  
Learning Algorithm ◽  
Forecast Model ◽  
Functional Networks ◽  
Non Linear ◽  
Linear Problems ◽  
Simulation Results ◽  
Forecast Function

Fitting of forecast function is very difficult and important in non-linear regression forecast problems. The accuracy is directly affected by the fitting of forecast function. Linear model replaced non-linear model in the traditional method is difficult to solve the problem when non-linear is stronger, and the result of fitting and forecast is not ideal. Functional network is a recently introduced extension of neural networks. It has certain advantages solving non-linear problems. Non-linear regression forecast model and learning algorithm based on functional networks is proposed in this article. Example about multi-variable non-linear regression forecast is provided. The simulation results demonstrate that forecast model based on Functional Networks whose accuracy of fitting and forecasting is more than some traditional methods have some value about theory and application.

scholarly journals The Application of Multiple Linear Regression and Artificial Neural Network Models for Yield Prediction of Very Early Potato Cultivars before Harvest

Agronomy ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 885
Author(s):  
Magdalena Piekutowska ◽  
Gniewko Niedbała ◽  
Tomasz Piskier ◽  
Tomasz Lenartowicz ◽  
Krzysztof Pilarski ◽  
...  
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Linear Model ◽  
Forecast Error ◽  
Linear Regression Analysis ◽  
Potato Cultivars ◽  
Forecast Errors ◽  
Early Potato ◽  
Non Linear ◽  
Artificial Neural

Yield forecasting is a rational and scientific way of predicting future occurrences in agriculture—the level of production effects. Its main purpose is reducing the risk in the decision-making process affecting the yield in terms of quantity and quality. The aim of the following study was to generate a linear and non-linear model to forecast the tuber yield of three very early potato cultivars: Arielle, Riviera, and Viviana. In order to achieve the set goal of the study, data from the period 2010–2017 were collected, coming from official varietal experiments carried out in northern and northwestern Poland. The linear model has been created based on multiple linear regression analysis (MLR), while the non-linear model has been built using artificial neural networks (ANN). The created models can predict the yield of very early potato varieties on 20th June. Agronomic, phytophenological, and meteorological data were used to prepare the models, and the correctness of their operation was verified on the basis of separate sets of data not participating in the construction of the models. For the proper validation of the model, six forecast error metrics were used: i.e., global relative approximation error (RAE), root mean square error (RMS), mean absolute error (MAE), and mean absolute percentage error (MAPE). As a result of the conducted analyses, the forecast error results for most models did not exceed 15% of MAPE. The predictive neural model NY1 was characterized by better values of quality measures and ex post forecast errors than the regression model RY1.

scholarly journals Biological scaling analyses are more than statistical line fitting

2021 ◽  
Vol 224 (11) ◽  
Author(s):  
Douglas S. Glazier
Keyword(s):  
Body Size ◽  
Linear Regression ◽  
Traditional Method ◽  
Biological Traits ◽  
Log Transformation ◽  
Size Scaling ◽  
Non Linear ◽  
Scaling Analyses ◽  
Log Linear ◽  
Best Fit

ABSTRACT The magnitude of many biological traits relates strongly and regularly to body size. Consequently, a major goal of comparative biology is to understand and apply these ‘size-scaling’ relationships, traditionally quantified by using linear regression analyses based on log-transformed data. However, recently some investigators have questioned this traditional method, arguing that linear or non-linear regression based on untransformed arithmetic data may provide better statistical fits than log-linear analyses. Furthermore, they advocate the replacement of the traditional method by alternative specific methods on a case-by-case basis, based simply on best-fit criteria. Here, I argue that the use of logarithms in scaling analyses presents multiple valuable advantages, both statistical and conceptual. Most importantly, log-transformation allows biologically meaningful, properly scaled (scale-independent) comparisons of organisms of different size, whereas non-scaled (scale-dependent) analyses based on untransformed arithmetic data do not. Additionally, log-based analyses can readily reveal biologically and theoretically relevant discontinuities in scale invariance during developmental or evolutionary increases in body size that are not shown by linear or non-linear arithmetic analyses. In this way, log-transformation advances our understanding of biological scaling conceptually, not just statistically. I hope that my Commentary helps students, non-specialists and other interested readers to understand the general benefits of using log-transformed data in size-scaling analyses, and stimulates advocates of arithmetic analyses to show how they may improve our understanding of scaling conceptually, not just statistically.

Used Car Price Estimation: Moving from Linear Regression towards a New S-Curve Model

2021 ◽  
Vol 22 (3) ◽  
pp. 1174-1187
Author(s):  
Fadzilah Salim ◽  
Nur Azman Abu
Keyword(s):  
Linear Regression ◽  
Linear Model ◽  
Real Life ◽  
Real Data ◽  
Prediction Errors ◽  
Curve Model ◽  
Non Linear ◽  
Used Car ◽  
S Curve ◽  
Used Cars

A simple linear regression is commonly used as a practical predictive model on a used car price. It is a useful model which carry smaller prediction errors around its central mean. Practically, real data will hardly produce a linear relationship. A non-linear model has been observed to better forecast any price appreciation and manage prediction errors in real-life phenomena. In this paper, an S-curve model shall be proposed as an alternative non-linear model in estimating the price of used cars. A dynamic S-shaped Membership Function (SMF) is used as a basis to build an S-curve pricing model in this research study. Real used car price data has been collected from a popular website. Comparisons against linear regression and cubic regression are made. An S-curve model has produced smaller error than linear regression while its residual is closer to a cubic regression. Overall, an S-curve model is anticipated to provide a better and more practical estimate on used car prices in Malaysia.

More Linear Models in R!

2021 ◽  
pp. 139-180
Author(s):  
Justin C. Touchon
Keyword(s):  
Linear Regression ◽  
Linear Model ◽  
Confidence Intervals ◽  
Linear Models ◽  
Analysis Of Covariance ◽  
Regression Curves ◽  
The World ◽  
Non Linear ◽  
Post Hoc

Chapter 6 continues exploring the world of statistics that are covered within the linear model, namely two-way and three-way ANOVA, linear regression and analysis of covariance (ANCOVA). In each type of model, a detailed description of how to interpret the summary output is undertaken, including understanding how to interpret and plot interactions. Conducting post-hoc analyses and using the predict() function are also covered. The chapter ends by reinforcing earlier plotting skills in ggplot2 by walking through an example of making a professional looking figure with multiple non-linear regression curves and confidence intervals.

scholarly journals Pulse Transit Time and Blood Pressure During Cardiopulmonary Exercise Tests

2014 ◽  
pp. 287-296 ◽  
Author(s):  
T. WIBMER ◽  
K. DOERING ◽  
C. KROPF-SANCHEN ◽  
S. RÜDIGER ◽  
I. BLANTA ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Linear Regression ◽  
Linear Model ◽  
Transit Time ◽  
Surrogate Marker ◽  
Pulse Transit Time ◽  
Additional Parameter ◽  
Exercise Tests ◽  
Cardiopulmonary Exercise ◽  
Non Linear

Pulse transit time (PTT), the interval between ventricular electrical activity and peripheral pulse wave, is assumed to be a surrogate marker for blood pressure (BP) changes. The objective of this study was to analyze PTT and its relation to BP during cardiopulmonary exercise tests (CPET). In 20 patients (mean age 51±18.4 years), ECG and finger-photoplethysmography were continuously recorded during routine CPETs. PTT was calculated for each R-wave in the ECG and the steepest slope of the corresponding upstroke in the plethysmogram. For each subject, linear and non-linear regression models were used to assess the relation between PTT and upper-arm oscillometric BP in 9 predefined measuring points including measurements at rest, during exercise and during recovery. Mean systolic BP (sBP) and PTT at rest were 128 mm Hg and 366 ms respectively, 197 mm Hg and 289 ms under maximum exercise, and 128 mm Hg and 371 ms during recovery. Linear regression showed a significant, strong negative correlation between PTT and sBP. The correlation between PTT and diastolic BP was rather weak. Bland-Altman plots of sBP values estimated by the regression functions revealed slightly better limits of agreements for the non-linear model (–10.9 to 10.9 mm Hg) than for the linear model (−13.2 to 13.1 mm Hg). These results indicate that PTT is a good potential surrogate measure for sBP during exercise and could easily be implemented in CPET as an additional parameter of cardiovascular reactivity. A non-linear approach might be more effective in estimating BP than linear regression.

Effects of Non-Linear Wheel Suspension Bushing on Vehicle Response

2012 ◽  
Author(s):  
Jenny Jerrelind ◽  
Ines Lopez Arteaga ◽  
Lars Drugge ◽  
Leif Kari
Keyword(s):  
Linear Model ◽  
Contact Force ◽  
Ground Contact ◽  
High Frequencies ◽  
Quarter Car Model ◽  
Car Model ◽  
Non Linear ◽  
Simulation Results ◽  
Quarter Car ◽  
Space Ratio

This work presents an analysis of the effects of non-linear characteristics of a top mount bushing in the wheel suspension of a vehicle when evaluating vehicle characteristics such as comfort and handling. The investigation is performed by comparing simulation results from a quarter car model when using a non-linear bushing model and an approximated linear bushing model. It is revealed when analysing the results that there are differences in the response when comparing measures such as sprung mass acceleration, rattle space ratio and tyre-ground contact force. The conclusion is that the more detailed bushing model mainly affects the acceleration levels especially at high frequencies where the linear model underestimates the acceleration. The rattle space ratio and tyre-ground contact force are also affected but not to the same extent.

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