On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

1993 ◽  
Vol 9 (3) ◽  
pp. 504-515 ◽  
Author(s):  
Kazuhiro Ohtani ◽  
Hikaru Hasegawa
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Important Variable ◽  
Small Sample ◽  
Small Samples ◽  
Coefficient Of Determination ◽  
Proxy Variables ◽  
Small Sample Properties ◽  
Multivariate T

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

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.

scholarly journals THREE-DIMENSIONAL POSTURE ESTIMATION OF FOOT BONES BY USING PLANTAR PLATE

2017 ◽  
Vol 20 (01) ◽  
pp. 1750011
Author(s):  
Kenta Nomura ◽  
Teru Yonezawa ◽  
Shinichi Kosugi ◽  
Yasuhito Tanaka ◽  
Hiroshi Mizoguchi ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Three Dimensional ◽  
Estimation Accuracy ◽  
Coefficient Of Determination ◽  
Plantar Plate ◽  
Foot Bones ◽  
Estimation Function ◽  
Almost All

Purpose: This paper proposes a method to easily and quantitatively estimate the changes in the foot bone three-dimensional (3D) posture from the 3D posture of a plantar plate without using X-ray or computed tomography (CT). Methods: The estimation functions from the posture of the plantar plate attached to the sole of a foot to the posture of the each bone are calculated using multiple regression analysis (MRA). Because we assumed that the posture of the plantar plate is related to each bone posture. Each bone posture can be estimated by substituting the plantar plate posture into the estimation function. Results: The adjusted coefficient of determination of the linear regression model (estimation function) of more than 90% was obtained by the estimation function, which was higher than 0.70. The estimation accuracy root mean square error (RMSE) of the translation and rotation were approximately within [Formula: see text][Formula: see text]mm and [Formula: see text], respectively. The RMSE/range of motion (RoM) values of the translation and rotation were approximately within [Formula: see text] and [Formula: see text], respectively. Conclusion: The experimental results suggest that the 3D posture of almost all types of foot bones can be easily estimated using plantar plate posture and the linear regression model. This is an inexpensive, easy-to-apply method that can perform real-time measurement.

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

scholarly journals Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Sajid Ali Khan ◽  
Sayyad Khurshid ◽  
Tooba Akhtar ◽  
Kashmala Khurshid
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Sample Size ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Small Samples ◽  
Sample Sizes

In this research we discusses to Ordinary Least Squares and Generalized Least Squares techniques and estimate with First Order Autoregressive scheme from different correlation levels by using simple linear regression model. A comparison has been made between these two methods on the basis of variances results. For the purpose of comparison, we use simulation of Monte Carlo study and the experiment is repeated 5000 times. We use sample sizes 50, 100, 200, 300 and 500, and observe the influence of different sample sizes on the estimators. By comparing variances of OLS and GLS at different values of sample sizes and correlation levels with , we found that variance of ( ) at sample size 500, OLS and GLS gives similar results but at sample size 50 variance of GLS ( ) has minimum values as compared to OLS. So it is clear that variance of GLS ( ) is best. Similarly variance of ( ) from OLS and GLS at sample size 500 and correlation -0.05 with , GLS give minimum value as compared to all other sample sizes and correlations. By comparing overall results of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS), we conclude that in large samples both are gives similar results but small samples GLS is best fitted as compared to OLS.

scholarly journals Predicting Virulence of Fusarium oxysporum f. sp. Cubense Based on the Production of Mycotoxin Using a Linear Regression Model

Toxins ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 254 ◽  
Author(s):  
Chuange Shao ◽  
Dandan Xiang ◽  
Hong Wei ◽  
Siwen Liu ◽  
Ganjun Yi ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Fusarium Oxysporum ◽  
Fusarium Wilt ◽  
Linear Regression Model ◽  
Fusaric Acid ◽  
Coefficient Of Determination ◽  
Banana Plant ◽  
Vegetative Compatibility Groups ◽  
Linearity Test

Fusarium wilt caused by Fusarium oxysporum f.sp. cubense (Foc) is one of the most destructive diseases for banana. For their risk assessment and hazard characterization, it is vital to quickly determine the virulence of Foc isolates. However, this usually takes weeks or months using banana plant assays, which demands a better approach to speed up the process with reliable results. Foc produces various mycotoxins, such as fusaric acid (FSA), beauvericin (BEA), and enniatins (ENs) to facilitate their infection. In this study, we developed a linear regression model to predict Foc virulence using the production levels of the three mycotoxins. We collected data of 40 Foc isolates from 20 vegetative compatibility groups (VCGs), including their mycotoxin profiles (LC-MS) and their plant disease index (PDI) values on Pisang Awak plantlets in greenhouse. A linear regression model was trained from the collected data using FSA, BEA and ENs as predictor variables and PDI values as the response variable. Linearity test statistics showed this model meets all linearity assumptions. We used all data to predict PDI with high fitness of the model (coefficient of determination (R2 = 0.906) and adjust coefficient (R2adj = 0.898)) indicating a strong predictive power of the model. In summary, we developed a linear regression model useful for the prediction of Foc virulence on banana plants from the quantification of mycotoxins in Foc strains, which will facilitate quick determination of virulence in newly isolated Foc emerging Fusarium wilt of banana epidemics threatening banana plantations worldwide.

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