scholarly journals The Distribution of the Coefficient of determination in Linear Regression Model: A Review

2021 ◽  
Vol 23 (09) ◽  
pp. 126-127
Author(s):  
El Houssainy A. Rady ◽  
◽  
Ahmed Amin El-Sheikh ◽  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Error Term ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Common Assumption ◽  
Normal Distributions ◽  
Error Terms

In this article, we review the different studies about the coefficient of determination in linear regression models and make a highlight about the inferences and the density function of the coefficient of determination which presented under the most common assumption when the error terms obey the normal distributions, and also analyzed the certain effects of departures from normality of the error term

Estimation in Dynamic Linear Regression Models with Infinite Variance Errors

1993 ◽  
Vol 9 (4) ◽  
pp. 570-588 ◽  
Author(s):  
Keith Knight
Keyword(s):  
Asymptotic Behavior ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Infinite Variance ◽  
Linear Regression Models ◽  
Asymptotically Normal ◽  
Second Moments ◽  
True Values

This paper considers the asymptotic behavior of M-estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n−½ rate.

scholarly journals Brazilian Articles in Top-Tier Dental Journals and Influence of International Collaboration on Citation Rates

2019 ◽  
Vol 30 (4) ◽  
pp. 307-316 ◽  
Author(s):  
Ana Paula R Gonçalves ◽  
Bruna L Porto ◽  
Bruna Rodolfo ◽  
Clovis M Faggion Jr ◽  
Bernardo A. Agostini ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
International Collaboration ◽  
Linear Regression Model ◽  
Regression Models ◽  
Dental Materials ◽  
Original Research ◽  
Linear Regression Models ◽  
Article Type ◽  
Multilevel Linear Regression

Abstract This study investigated the presence of co-authorship from Brazil in articles published in top-tier dental journals and analyzed the influence of international collaboration, article type (original research or review), and funding on citation rates. Articles published between 2015 and 2017 in 38 selected journals from 14 dental subareas were screened in Scopus. Bibliographic information, citation counts, and funding details were recorded for all articles (N=15619). Collaboration with other top-10 publishing countries in dentistry was registered. Annual citations averages (ACA) were calculated. A linear regression model assessed differences in ACA between subareas. Multilevel linear regression models evaluated the influence of article type, funding, and presence of international collaboration in ACA. Brazil was a frequent co-author of articles published in the period (top 3: USA=25.5%; Brazil=13.8%; Germany=9.2%) and the country with most publications in two subareas. The subjects with the biggest share of Brazil are Operative Dentistry/Cariology, Dental Materials, and Endodontics. Brazil was second in total citations, but fifth in citation averages per article. From the total of 2155 articles co-authored by Brazil, 74.8% had no co-authorship from other top-10 publishing countries. USA (17.8%), Italy (4.2%), and UK (3.2%) were the main co-author countries, but the main collaboration country varied between subjects. Implantology and Dental Materials were the subjects with most international co-authorship. Review articles and articles with international collaboration were associated with increased citation rates, whereas the presence of study funding did not influence the citations.

scholarly journals Significant non-linearity in nitrous oxide chamber data and its effect on calculated annual emissions

2009 ◽  
Vol 6 (1) ◽  
pp. 115-141 ◽  
Author(s):  
P. C. Stolk ◽  
C. M. J. Jacobs ◽  
E. J. Moors ◽  
A. Hensen ◽  
G. L. Velthof ◽  
...  
Keyword(s):  
Nitrous Oxide ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Surface Fluxes ◽  
Linear Regression Models ◽  
Open Questions ◽  
Non Linear

Abstract. Chambers are widely used to measure surface fluxes of nitrous oxide (N2O). Usually linear regression is used to calculate the fluxes from the chamber data. Non-linearity in the chamber data can result in an underestimation of the flux. Non-linear regression models are available for these data, but are not commonly used. In this study we compared the fit of linear and non-linear regression models to determine significant non-linearity in the chamber data. We assessed the influence of this significant non-linearity on the annual fluxes. For a two year dataset from an automatic chamber we calculated the fluxes with linear and non-linear regression methods. Based on the fit of the methods 32% of the data was defined significant non-linear. Significant non-linearity was not recognized by the goodness of fit of the linear regression alone. Using non-linear regression for these data and linear regression for the rest, increases the annual flux with 21% to 53% compared to the flux determined from linear regression alone. We suggest that differences this large are due to leakage through the soil. Macropores or a coarse textured soil can add to fast leakage from the chamber. Yet, also for chambers without leakage non-linearity in the chamber data is unavoidable, due to feedback from the increasing concentration in the chamber. To prevent a possibly small, but systematic underestimation of the flux, we recommend comparing the fit of a linear regression model with a non-linear regression model. The non-linear regression model should be used if the fit is significantly better. Open questions are how macropores affect chamber measurements and how optimization of chamber design can prevent this.

scholarly journals A Study on Misspecification and Predictive Accuracy of Stochastic Linear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 532
Author(s):  
C. Narayana ◽  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Predictive Accuracy ◽  
Response Prediction ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Research Article ◽  
Lm Test

The present study research article proposes a modified test for misspecification of the stochastic linear regression model and a new test for predictive accuracy of stochastic linear regression model. In addition to this modified Lagrange Multiplier (LM) test for misspecification of stochastic linear regression has been developed. In the derivation of the test statistics internally studentized residuals have been used. William A. Branch et.al [1] presented a stochastic non-linear self-referential model in which expectations are based on linear perceptions. I.sh. Torgovitski et.al [2] in this paper discussed the problem of raising the efficiency of the regression coefficients estimation as suggested an approach which allows as to reduce mathematical expectations of the square of deviation of the response prediction. 

Prediction in Two­Equation Linear Regression Models

2005 ◽  
Vol 57 (3-4) ◽  
pp. 195-208
Author(s):  
Amitava Dey ◽  
V. K. Sharma ◽  
Himadri Ghosh
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Regression Models ◽  
Time Series Data ◽  
Generalized Least Squares ◽  
Series Data ◽  
Linear Regression Models ◽  
Error Terms ◽  
Best Linear Unbiased

In regression models using time series data, the errors are generally correlated. The sample residuals contain useful information for predicting post­sample observations. This information, which is generally ignored, has been exploited here in deriving the best linear unbiased predictors in a 2­equation linear regression model. The gain in efficiency of the proposed predictors over the usual generalized least ­ squares predictors has been obtained and the particular case when error terms in the two equations follow AR(l) process has also been disscussed.

scholarly journals Multi-criteria approach to pair-multiple linear regression models constructing

2021 ◽  
Vol 21 (1) ◽  
pp. 88-99
Author(s):  
Mikhail P. Bazilevskiy ◽  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Multiple Regression ◽  
Linear Regression Model ◽  
Regression Models ◽  
Multiple Linear Regression Model ◽  
Linear Regression Models ◽  
Deming Regression ◽  
Multiple Linear Regression Models

A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable. An aggregated quality criterion of regression models based on four well-known indicators: the coefficient of determination, Darbin – Watson, the consistency of behaviour and the average relative error of approximation is proposed. Using this criterion, the problem of multi-criteria construction of a pair-multiple linear regression model is formalized as a nonlinear programming problem. An algorithm for its approximate solution is developed. The results of this work can be used to improve the overall qualitative characteristics of multiple linear regression models.

scholarly journals A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1422
Author(s):  
Maryam Al-Kandari ◽  
Kingsley Adjenughwure ◽  
Kyriakos Papadopoulos
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Fuzzy Number ◽  
Regression Models ◽  
Tolerance Interval ◽  
Linear Regression Models ◽  
Fuzzy Linear Regression ◽  
The Mean ◽  
Statistical Tolerance

Linear regression is a simple but powerful tool for prediction. However, it still suffers from some deficiencies, which are related to the assumptions made when using a model like normality of residuals, uncorrelated errors, where the mean of residuals should be zero. Sometimes these assumptions are violated or partially violated, thereby leading to uncertainties or unreliability in the predictions. This paper introduces a new method to account for uncertainty in the residuals of a linear regression model. First, the error in the estimation of the dependent variable is calculated and transformed to a fuzzy number, and this fuzzy error is then added to the original crisp prediction, thereby resulting in a fuzzy prediction. The results are compared to a fuzzy linear regression with crisp input and fuzzy output, in terms of their ability to represent uncertainty in prediction.

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.

Whole Facility Measurement for Quantifying Energy Saving in an Office Building, Malaysia

2015 ◽  
Vol 785 ◽  
pp. 676-681 ◽  
Author(s):  
Nor Shahida Razali ◽  
Nofri Yenita Dahlan
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Energy Saving ◽  
Linear Regression Model ◽  
Energy Use ◽  
Multiple Linear Regression Model ◽  
Office Building ◽  
Coefficient Of Determination ◽  
Independent Variable

This paper presents the concept of International Performance Measurement and Verification Protocol (IPMVP) for determining energy saving at whole facility level for an office building in Malaysia. Regression analysis is used to develop baseline model from a set of baseline data which correlates baseline energy with appropriate independents variables, i.e. Cooling Degree Days (CDD) and Number of Working Days (NWD) in this paper. In determining energy savings, the baseline energy is adjusted to the same set condition of reporting period using energy cost avoidance approach. Two types of energy saving analyses have been presented in the case study; 1) Single linear regression for each independent variable, 2) Multiple linear regression for each independent variable. Results show that NWD has coefficient of determination, R2 higher than CDD which indicates that NWD has stronger correlation with the energy use than CDD in the building. Finding also shows that the R2 for multiple linear regression model are higher than single linear regression model. This shows the fact that more than one component are affecting the energy use in the building.

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