On the coefficient of determination for mixed regression models

2008 ◽  
Vol 138 (10) ◽  
pp. 3022-3038 ◽  
Author(s):  
Ola Hössjer
Keyword(s):  
Regression Models ◽  
Coefficient Of Determination ◽  
Mixed Regression

scholarly journals A NON-DESTRUCTIVE METHOD FOR ESTIMATING LEAF AREA OF Ceiba glaziovii (Kuntze) K. Schum.

FLORESTA ◽  
2019 ◽  
Vol 50 (1) ◽  
pp. 1063
Author(s):  
João Everthon da Silva Ribeiro ◽  
Francisco Romário Andrade Figueiredo ◽  
Ester Dos Santos Coêlho ◽  
Walter Esfrain Pereira ◽  
Manoel Bandeira de Albuquerque
Keyword(s):  
Leaf Area ◽  
Regression Models ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Linear Measurements ◽  
Maximum Width ◽  
Bias Index ◽  
Different Shapes ◽  
Non Destructive

The determination of leaf area is of fundamental importance in studies involving ecological and ecophysiological aspects of forest species. The objective of this research was to adjust an equation to determine the leaf area of Ceiba glaziovii as a function of linear measurements of leaves. Six hundred healthy leaf limbs were collected in different matrices, with different shapes and sizes, in the Mata do Pau-Ferro State Park, Areia, Paraíba state, Northeast Brazil. The maximum length (L), maximum width (W), product between length and width (L.W), and leaf area of the leaf limbs were calculated. The regression models used to construct equations were: linear, linear without intercept, quadratic, cubic, power and exponential. The criteria for choosing the best equation were based on the coefficient of determination (R²), Akaike information criterion (AIC), root mean square error (RMSE), Willmott concordance index (d) and BIAS index. All the proposed equations satisfactorily estimate the leaf area of C. glaziovii, due to their high determination coefficients (R² ≥ 0.851). The linear model without intercept, using the product between length and width (L.W), presented the best criteria to estimate the leaf area of the species, using the equation 0.4549*LW.

scholarly journals Non-Linear Regression Models with Vibration Amplitude Optimization Algorithms in a Microturbine

Sensors ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 130
Author(s):  
Omar Rodríguez-Abreo ◽  
Juvenal Rodríguez-Reséndiz ◽  
L. A. Montoya-Santiyanes ◽  
José Manuel Álvarez-Alvarado
Keyword(s):  
Linear Regression ◽  
Vibration Amplitude ◽  
Regression Models ◽  
Engineering Problem ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Gray Wolf ◽  
Linear Regression Models ◽  
Machinery Condition Monitoring ◽  
Non Linear

Machinery condition monitoring and failure analysis is an engineering problem to pay attention to among all those being studied. Excessive vibration in a rotating system can damage the system and cannot be ignored. One option to prevent vibrations in a system is through preparation for them with a model. The accuracy of the model depends mainly on the type of model and the fitting that is attained. The non-linear model parameters can be complex to fit. Therefore, artificial intelligence is an option for performing this tuning. Within evolutionary computation, there are many optimization and tuning algorithms, the best known being genetic algorithms, but they contain many specific parameters. That is why algorithms such as the gray wolf optimizer (GWO) are alternatives for this tuning. There is a small number of mechanical applications in which the GWO algorithm has been implemented. Therefore, the GWO algorithm was used to fit non-linear regression models for vibration amplitude measurements in the radial direction in relation to the rotational frequency in a gas microturbine without considering temperature effects. RMSE and R2 were used as evaluation criteria. The results showed good agreement concerning the statistical analysis. The 2nd and 4th-order models, and the Gaussian and sinusoidal models, improved the fit. All models evaluated predicted the data with a high coefficient of determination (85–93%); the RMSE was between 0.19 and 0.22 for the worst proposed model. The proposed methodology can be used to optimize the estimated models with statistical tools.

MATHEMATICAL MODELING OF TELEROENTGENOGRAPHIC PARAMETERS ACCORDING TO THE METHOD OF SCHWARZ A. M. DEPENDING ON THE BASIC CEPHALOMETRIC PARAMETERS IN UKRAINIAN YOUNG MEN AND YOUNG WOMEN WITH DIFFERENT FACE TYPES

2021 ◽  
Vol 74 (6) ◽  
pp. 1488-1492
Author(s):  
Аlla V. Маrchenko ◽  
Oleksandr S. Prokopenko ◽  
Іryna V. Dzevulska ◽  
Tatyana R. Zakalata ◽  
Igor V. Gunas
Keyword(s):  
Young Women ◽  
Regression Models ◽  
Young Men ◽  
Cone Beam ◽  
Coefficient Of Determination ◽  
Normal Occlusion ◽  
Different Types ◽  
Dental Intervention ◽  
Individualized Approach ◽  
Facial Types

The aim: Is development and analysis of regression models of teleroentgenographic indices according to Schwarz A. M., which can be adjusted during surgery depending on the parameters that usually do not change in Ukrainian young men and young women with with normal occlusion close to orthognathic occlusion and different facial types. Materials and methods: Teleroentgenographic indices were obtained using a dental cone-beam tomograph Veraviewepocs 3D Morita and studied in 49 young men and 76 young women with normal occlusion close to orthognathic. Persons were divided into groups with different face types according to the recommendations of Schwarz A. M. In the license package “Statistica 6.0”, regression models of teleroentgenographic indices were built according to Schwarz A. M. Results: For young men with orthognathic occlusion and with different types of faces according to Schwarz A. M. constructed 10 of 27 possible reliable regression models of the group of teleroentgenographic indicators, which can be corrected during surgical, orthopedic interventions in dentistry depending on the group of basic, invariable cephalometric indicators greater than 0.6 (R2 = from 0.609 to 0.996); and in young women with different face types, 8 of the 27 possible reliable regression models in which the coefficient of determination is greater than 0.6 (R2 = from 0.642 to 0.986). Conclusions: The developed regression models provide the most individualized approach in determining the method and scope of the required dental intervention.

Evaluating the Statistical Significance of Models Developed by Stepwise Regression

1983 ◽  
Vol 20 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Shelby H. McIntyre ◽  
David B. Montgomery ◽  
V. Srinivasan ◽  
Barton A. Weitz
Keyword(s):  
Monte Carlo ◽  
Null Hypothesis ◽  
Regression Models ◽  
Stepwise Regression ◽  
Statistical Significance ◽  
Selection Procedure ◽  
Coefficient Of Determination ◽  
Forward Selection ◽  
Monte Carlo Simulation Study ◽  
Independent Variables

Information for evaluating the statistical significance of stepwise regression models developed with a forward selection procedure is presented. Cumulative distributions of the adjusted coefficient of determination ([Formula: see text]) under the null hypothesis of no relationship between the dependent variable and m potential independent variables are derived from a Monté Carlo simulation study. The study design included sample sizes of 25, 50, and 100, available independent variables of 10, 20, and 40, and three criteria for including variables in the regression model. The results reveal that the biases involved in testing statistical significance by two well-known rules are very large, thus demonstrating the desirability of using the Monté Carlo cumulative [Formula: see text] distributions developed by the authors. Although the results were derived under the assumption of uncorrelated predictors, the authors show that the results continue to be useful for the correlated predictor case.

scholarly journals Air Quality Index and Air Pollutant Concentration Prediction Based on Machine Learning Algorithms

2019 ◽  
Vol 9 (19) ◽  
pp. 4069 ◽  
Author(s):  
Huixiang Liu ◽  
Qing Li ◽  
Dongbing Yu ◽  
Yu Gu
Keyword(s):  
Machine Learning ◽  
Air Pollution ◽  
Air Quality ◽  
Regression Models ◽  
Quality Index ◽  
Air Pollutant ◽  
Air Quality Index ◽  
Machine Learning Algorithms ◽  
Coefficient Of Determination ◽  
Support Vector

Air pollution has become an important environmental issue in recent decades. Forecasts of air quality play an important role in warning people about and controlling air pollution. We used support vector regression (SVR) and random forest regression (RFR) to build regression models for predicting the Air Quality Index (AQI) in Beijing and the nitrogen oxides (NOX) concentration in an Italian city, based on two publicly available datasets. The root-mean-square error (RMSE), correlation coefficient (r), and coefficient of determination (R2) were used to evaluate the performance of the regression models. Experimental results showed that the SVR-based model performed better in the prediction of the AQI (RMSE = 7.666, R2 = 0.9776, and r = 0.9887), and the RFR-based model performed better in the prediction of the NOX concentration (RMSE = 83.6716, R2 = 0.8401, and r = 0.9180). This work also illustrates that combining machine learning with air quality prediction is an efficient and convenient way to solve some related environment problems.

Global observation-based climatology of precipitation occurrence and peak intensity

2020 ◽  
Author(s):  
Hylke Beck ◽  
Seth Westra ◽  
Eric Wood
Keyword(s):  
Land Surface ◽  
Regression Models ◽  
Cross Validation ◽  
Climate Models ◽  
Daily Precipitation ◽  
State Of The Art ◽  
Coefficient Of Determination ◽  
Peak Intensity ◽  
Uncertainty Estimates ◽  
Fold Cross Validation

<p>We introduce a unique set of global observation-based climatologies of daily precipitation (<em>P</em>) occurrence (related to the lower tail of the <em>P</em> distribution) and peak intensity (related to the upper tail of the <em>P</em> distribution). The climatologies were produced using Random Forest (RF) regression models trained with an unprecedented collection of daily <em>P</em> observations from 93,138 stations worldwide. Five-fold cross-validation was used to evaluate the generalizability of the approach and to quantify uncertainty globally. The RF models were found to provide highly satisfactory performance, yielding cross-validation coefficient of determination (<em>R</em><sup>2</sup>) values from 0.74 for the 15-year return-period daily <em>P</em> intensity to 0.86 for the >0.5 mm d<sup>-1</sup> daily <em>P</em> occurrence. The performance of the RF models was consistently superior to that of state-of-the-art reanalysis (ERA5) and satellite (IMERG) products. The highest <em>P</em> intensities over land were found along the western equatorial coast of Africa, in India, and along coastal areas of Southeast Asia. Using a 0.5 mm d<sup>-1</sup> threshold, <em>P</em> was estimated to occur 23.2 % of days on average over the global land surface (excluding Antarctica). The climatologies including uncertainty estimates will be released as the Precipitation DISTribution (PDIST) dataset via www.gloh2o.org/pdist. We expect the dataset to be useful for numerous purposes, such as the evaluation of climate models, the bias correction of gridded <em>P</em> datasets, and the design of hydraulic structures in poorly gauged regions.</p>

scholarly journals Comparison of Methods for Harvest Prediction in ‘Gigante’ Cactus Pear

2019 ◽  
Vol 11 (14) ◽  
pp. 216 ◽  
Author(s):  
Bruno V. C. Guimarães ◽  
Sérgio L. R. Donato ◽  
Ignacio Aspiazú ◽  
Alcinei M. Azevedo ◽  
Abner J. de Carvalho
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Regression Models ◽  
Coefficient Of Determination ◽  
Cactus Pear ◽  
Federal Institute ◽  
The Mean ◽  
Artificial Neural

Behavior analysis and plant expression are the answers the researcher needs to construct predictive models that minimize the effects of the uncertainties of field production. The objective of this study was to compare the simple and multiple linear regression methods and the artificial neural networks to allow the maximum security in the prediction of harvest in ‘Gigante’ cactus pear. The uniformity test was conducted at the Federal Institute of Bahia, Campus Guanambi, Bahia, Brazil, coordinates 14°13′30″ S, 42°46′53″ W and altitude of 525 m. At 930 days after planting, we evaluated 384 basic units, in which were measured the following variables: plant height (PH); cladode length (CL), width (CW) and thickness (CT); cladode number (CN); total cladode area (TCA); cladode area (CA) and cladode yield (Y). For the comparison between the artificial neural networks (ANN) and regression models (single and multiple-SLR and MLR), we considered the mean prediction error (MPE), the mean quadratic error (MQE), the mean square of deviation (MSD) and the coefficient of determination (R2).The values estimated by the ANN 7-5-1 showed the best proximity to the data obtained in field conditions, followed by ANN 6-2-1, MLR (TCA and CT), SLR (TCA) and SLR (CN). In this way, the ANN models with the topologies 7-2-1 and 6-2-1, MLR with the variables total cladode area and cladode thickness and SLR with the isolated descriptors total cladode area and cladode number, explain 85.1; 81.5; 76.3; 74.09 and 65.87%, respectively, of the yield variation. The ANNs were more efficient at predicting the yield of the ‘Gigante’ cactus pear when compared to the simple and multiple linear regression models.

Sign in / Sign up

Export Citation Format

Share Document