scholarly journals Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 856
Author(s):  
Vera Lucia Damasceno Tomazella ◽  
Sandra Rêgo Jesus ◽  
Amanda Buosi Gazon ◽  
Francisco Louzada ◽  
Saralees Nadarajah ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Real Data ◽  
Diagnostic Techniques ◽  
Reference Prior ◽  
Artificial Data ◽  
Jeffreys Prior ◽  
Reference Analysis ◽  
Leibler Divergence

This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior returned an improper one. The inferential purposes were obtained via Markov Chain Monte Carlo (MCMC). Furthermore, diagnostic techniques based on the Kullback–Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil.

scholarly journals Solving Multicollinearity Problem in Linear Regression Model: The Review Suggests New Idea of Partitioning and Extraction of the Explanatory Variables

2021 ◽  
Vol 2 (1) ◽  
pp. 12-20
Author(s):  
Kayode Ayinde, Olusegun O. Alabi ◽  
Ugochinyere Ihuoma Nwosu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Real Data ◽  
Least Square ◽  
Model Parameters ◽  
Explanatory Variables ◽  
Ordinary Least Square ◽  
Wide Range ◽  
High Level

Multicollinearity has remained a major problem in regression analysis and should be sustainably addressed. Problems associated with multicollinearity are worse when it occurs at high level among regressors. This review revealed that studies on the subject have focused on developing estimators regardless of effect of differences in levels of multicollinearity among regressors. Studies have considered single-estimator and combined-estimator approaches without sustainable solution to multicollinearity problems. The possible influence of partitioning the regressors according to multicollinearity levels and extracting from each group to develop estimators that will estimate the parameters of a linear regression model when multicollinearity occurs is a new econometrics idea and therefore requires attention. The results of new studies should be compared with existing methods namely principal components estimator, partial least squares estimator, ridge regression estimator and the ordinary least square estimators using wide range of criteria by ranking their performances at each level of multicollinearity parameter and sample size. Based on a recent clue in literature, it is possible to develop innovative estimator that will sustainably solve the problem of multicollinearity through partitioning and extraction of explanatory variables approaches and identify situations where the innovative estimator will produce most efficient result of the model parameters. The new estimator should be applied to real data and popularized for use.

scholarly journals Detecting Outliers In Multiple Linear Regression

2011 ◽  
Vol 17 (64) ◽  
pp. 9
Author(s):  
ايهاب عبد السلام
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Standard Error ◽  
Multiple Linear Regression Model ◽  
Real Data

It is well-known that the existence of outliers in the data will adversely affect the efficiency of estimation and results of the current study. In this paper four methods will be studied to detect outliers for the multiple linear regression model in two cases :  first, in real data; and secondly,  after adding the outliers to data and the attempt to detect it. The study is conducted for samples with different sizes, and uses three measures for  comparing between these methods . These three measures are : the mask, dumping and standard error of the estimate.

scholarly journals Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

2021 ◽  
Vol 20 (3) ◽  
pp. 425-449
Author(s):  
Haruka Murayama ◽  
Shota Saito ◽  
Yuji Iikubo ◽  
Yuta Nakahara ◽  
Toshiyasu Matsushima
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Real Data ◽  
Number Of Clusters ◽  
Bayes Prediction ◽  
Data Generating Process ◽  
Probabilistic Structure ◽  
Selection Of

AbstractPrediction based on a single linear regression model is one of the most common way in various field of studies. It enables us to understand the structure of data, but might not be suitable to express the data whose structure is complex. To express the structure of data more accurately, we make assumption that the data can be divided in clusters, and has a linear regression model in each cluster. In this case, we can assume that each explanatory variable has their own role; explaining the assignment to the clusters, explaining the regression to the target variable, or being both of them. Introducing probabilistic structure to the data generating process, we derive the optimal prediction under Bayes criterion and the algorithm which calculates it sub-optimally with variational inference method. One of the advantages of our algorithm is that it automatically weights the probabilities of being each number of clusters in the process of the algorithm, therefore it solves the concern about selection of the number of clusters. Some experiments are performed on both synthetic and real data to demonstrate the above advantages and to discover some behaviors and tendencies of the algorithm.

scholarly journals Fast Improvised Influential Distance for the Identification of Influential Observations in Multiple Linear Regression

2021 ◽  
Vol 50 (7) ◽  
pp. 2085-2094
Author(s):  
Habshah Midi ◽  
Muhammad Sani ◽  
Shelan Saied Ismaeel ◽  
Jayanthi Arasan
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Real Data ◽  
Initial Step ◽  
Influential Observations ◽  
Monte Carlo Simulation Study ◽  
Running Time

Influential observations (IO) are those observations that are responsible for misleading conclusions about the fitting of a multiple linear regression model. The existing IO identification methods such as influential distance (ID) is not very successful in detecting IO. It is suspected that the ID employed inefficient method with long computational running time for the identification of the suspected IO at the initial step. Moreover, this method declares good leverage observations as IO, resulting in misleading conclusion. In this paper, we proposed fast improvised influential distance (FIID) that can successfully identify IO, good leverage observations, and regular observations with shorter computational running time. Monte Carlo simulation study and real data examples show that the FIID correctly identify genuine IO in multiple linear regression model with no masking and a negligible swamping rate.

Physico-Chemical Analysis of Groundwater and Effect of Climatic Change in Angul-Talcher Area

2018 ◽  
Vol 6 (12) ◽  
pp. 26
Author(s):  
Aliva Bera ◽  
D.P. Satapathy
Keyword(s):  
Water Resources ◽  
Linear Regression ◽  
Regression Model ◽  
Climatic Change ◽  
Linear Regression Model ◽  
Ann Model ◽  
Quality Of Water ◽  
Physico Chemical ◽  
Simulation Based

In this paper, the linear regression model using ANN and the linear regression model using MS Excel were developed to estimate the physico-chemical concentrations in groundwater using pH, EC, TDS, TH, HCO3 as input parameters and Ca, Mg and K as output parameters. A comparison was made which indicated that ANN model had the better ability to estimate the physic-chemical concentrations in groundwater. An analytical survey along with simulation based tests for finding the climatic change and its effect on agriculture and water bodies in Angul-Talcher area is done. The various seasonal parameters such as pH, BOD, COD, TDS,TSS along with heavy elements like Pb, Cd, Zn, Cu, Fe, Mn concentration in water resources has been analyzed. For past 30 years rainfall data has been analyzed and water quality index values has been studied to find normal and abnormal quality of water resources and matlab based simulation has been done for performance analysis. All results has been analyzed and it is found that the condition is stable. 

Prediction of Surface Roughness and Optimization of Cutting Parameters in CNC Turning of Rotational Features

2020 ◽  
Vol 38 (8A) ◽  
pp. 1143-1153
Author(s):  
Yousif K. Shounia ◽  
Tahseen F. Abbas ◽  
Raed R. Shwaish
Keyword(s):  
Surface Roughness ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Feed Rate ◽  
Cutting Parameters ◽  
Spindle Speed ◽  
Depth Of Cut ◽  
Non Linear ◽  
Optimization Of Cutting Parameters

This research presents a model for prediction surface roughness in terms of process parameters in turning aluminum alloy 1200. The geometry to be machined has four rotational features: straight, taper, convex and concave, while a design of experiments was created through the Taguchi L25 orthogonal array experiments in minitab17 three factors with five Levels depth of cut (0.04, 0.06, 0.08, 0.10 and 0.12) mm, spindle speed (1200, 1400, 1600, 1800 and 2000) r.p.m and feed rate (60, 70, 80, 90 and 100) mm/min. A multiple non-linear regression model has been used which is a set of statistical extrapolation processes to estimate the relationships input variables and output which the surface roughness which prediction outside the range of the data. According to the non-linear regression model, the optimum surface roughness can be obtained at 1800 rpm of spindle speed, feed-rate of 80 mm/min and depth of cut 0.04 mm then the best surface roughness comes out to be 0.04 μm at tapper feature at depth of cut 0.01 mm and same spindle speed and feed rate pervious which gives the error of 3.23% at evolution equation.

An Enhanced Multiple Linear Regression Model for Seasonal Rainfall Prediction

2020 ◽  
Vol 10 (4) ◽  
pp. 473-483
Author(s):  
Pundra Chandra Shaker Reddy ◽  
Alladi Sureshbabu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Weather Prediction ◽  
Big Data Analytics ◽  
Multiple Linear Regression Model ◽  
Seasonal Rainfall ◽  
Climate Data ◽  
Rainfall Forecasting

Aims & Background: India is a country which has exemplary climate circumstances comprising of different seasons and topographical conditions like high temperatures, cold atmosphere, and drought, heavy rainfall seasonal wise. These utmost varieties in climate make us exact weather prediction is a challenging task. Majority people of the country depend on agriculture. Farmers require climate information to decide the planting. Weather prediction turns into an orientation in farming sector to deciding the start of the planting season and furthermore quality and amount of their harvesting. One of the variables are influencing agriculture is rainfall. Objectives & Methods: The main goal of this project is early and proper rainfall forecasting, that helpful to people who live in regions which are inclined natural calamities such as floods and it helps agriculturists for decision making in their crop and water management using big data analytics which produces high in terms of profit and production for farmers. In this project, we proposed an advanced automated framework called Enhanced Multiple Linear Regression Model (EMLRM) with MapReduce algorithm and Hadoop file system. We used climate data from IMD (Indian Metrological Department, Hyderabad) in 1901 to 2002 period. Results: Our experimental outcomes demonstrate that the proposed model forecasting the rainfall with better accuracy compared with other existing models. Conclusion: The results of the analysis will help the farmers to adopt effective modeling approach by anticipating long-term seasonal rainfall.

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