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 Inference in Multiple Linear Regression Model with Generalized Secant Hyperbolic Distribution Errors

2021 ◽  
Vol 17 (33) ◽  
pp. 45-70
Author(s):  
Álvaro Alexander Burbano Moreno ◽  
Oscar Orlando Melo-Martinez ◽  
M Qamarul Islam
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square ◽  
Model Parameters ◽  
Modified Maximum Likelihood ◽  
Test Of Hypothesis

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. We derive the estimators of model parameters by using modified maximum likelihood methodology and explore the properties of the modified maximum likelihood estimators so obtained. We show that the proposed estimators are more efficient and robust than the commonly used least square estimators. We also develop the relevant test of hypothesis procedures and compared the performance of such tests vis-a-vis the classical tests that are based upon the least square approach.

scholarly journals Inference in Multiple Linear Regression Model with Generalized Secant Hyperbolic Distribution Errors

2021 ◽  
Vol 17 (33) ◽  
pp. 45-70
Author(s):  
Álvaro Alexander Burbano Moreno ◽  
Oscar Orlando Melo-Martinez ◽  
Q Qamarul Islam
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square ◽  
Model Parameters ◽  
Modified Maximum Likelihood ◽  
Test Of Hypothesis

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. We derive the estimators of model parameters by using modified maximum likelihood methodology and explore the properties of the modified maximum likelihood estimators so obtained. We show that the proposed estimators are more efficient and robust than the commonly used least square estimators. We also develop the relevant test of hypothesis procedures and compared the performance of such tests vis-a-vis the classical tests that are based upon the least square approach.

Pengaruh pertumbuhan ekonomi, inflasi dan pengangguran terhadap tingkat kemiskinan di Sumatera Selatan

2019 ◽  
Vol 16 (1) ◽  
pp. 1-10
Author(s):  
Novegya Ratih Primandari
Keyword(s):  
Economic Growth ◽  
Time Series ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Time Series Data ◽  
Secondary Data ◽  
Poverty Rate ◽  
Least Square ◽  
Series Data ◽  
Ordinary Least Square

This research aims to analyze effect of economic growth, inflation and Unemployment on the Rate of Poverty in the Province of South Sumatera. This research used secondary data in the form of time series data from 2001-2017. The method used quantitative approach by applying a linear regression model with OLS estimation Ordinary Least Square (OLS) method. The results of this study indicate that partially and simultaneously Economic Growth, Inflation and Unemployment have a significant effect on the Poverty Rate in the Province of South Sumatera.

scholarly journals Statistical Modelling of the Capital Asset Pricing Model (CAPM)

2018 ◽  
Vol 7 (2) ◽  
pp. 146
Author(s):  
Silvi Qemo ◽  
Eahab Elsaid
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Statistical Modelling ◽  
Expected Returns ◽  
Explanatory Variables ◽  
Bid Ask Spread ◽  
Model Average

The purpose of this study is to derive a multiple linear regression model of the CAPM. More specifically, to test for other potential explanatory variables that can be added to the basic linear regression model for the expected returns on Apple Inc. The following explanatory variables were examined: share volume, outstanding shares, closing bid/ask spread, high/low spread and average spread. Using daily returns of Apple Inc. stock from 2007 till 2014 we were able to create a multiple linear regression model of CAPM that increase the R2 value from the basic linear regression model and enhances the amount of variability in the returns on an asset. This is an important modification that can help better forecast returns on assets.Keywords: CAPM; multiple linear regression model; average spread; variability in the returns

scholarly journals ANALISIS FAKTOR - FAKTOR YANG MEMPENGARUHI HARGA TANAH UNTUK PENGGUNAAN PERUMAHAN (STUDI KASUS: KECAMATAN BANYUMANIK)

2017 ◽  
Vol 5 (1) ◽  
pp. 57
Author(s):  
Triana Kurniwati ◽  
Bagio Mudakir
Keyword(s):  
Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square Method ◽  
Research Area ◽  
Least Square ◽  
City Center ◽  
Land Price ◽  
Ordinary Least Square ◽  
The City

Semarang city is densely populated that demand of settlement will increase continually, but land in city center is very limited and even it is scarce, therefore the land price which is placed in city center is high. That is why many inhabitant of Semarang city prefer to live in outskirts of the city. The shifting of land demand to the outskirts is also followed by increasing of land price in outskirts, it causes the land price in outskirts is uncontrolled.The research takes location in Banyumanik area. This research area consists of 7 districts, that are Jabungan, Pudak Payung, Banyumanik, Srondol Kulon, Pedalangan, Ngesrep, and Gedawang district. The sample total is one hundred (100). The data is analyzed by using multiple linear regression model with ordinary least square method (OLS).

scholarly journals Perbandingan Model Estimasi Artificial Neural Network Optimasi Genetic Algorithm dan Regresi Linier Berganda

2017 ◽  
Vol 10 (1) ◽  
pp. 13
Author(s):  
Jimmy Saputra Sebayang ◽  
Budi Yuniarto
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Artificial Neural Network ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square ◽  
Simulation Data ◽  
Ordinary Least Square

Multiple Linear Regression is a statistical approach most commonly used in performing predictive data modeling. One of the methods that can be used in estimating the parameters of the model on Multiple Linear Regression is Ordinary Least Square. It has classical assumptions requirements and often the assumptions are not satisfied. Another method that can be used as an alternative data modeling is Artificial Neural Network. It is  a free-distribution estimator because there's no assumptions that have to be satisfied.  However, modeling data using ANN has some problems such as selection of network topology, learning parameters and weight initialization. Genetic Algorithm method can be used to solve those problems. A set of simulation data was generated to test the reliability of ANN-GA model compared to Multiple Linear Regression model. Model comparison experiments indicate that ANN-GA model are better than Multiple Linear Regression model for estimating simulation data both on the data training and data testing.Keywords:Neural Network, Genetic Algorithm, Ordinary Least Square

ASYMPTOTIC THEORY FOR M-ESTIMATORS OVER A CONVEX KERNEL

1998 ◽  
Vol 14 (4) ◽  
pp. 387-422 ◽  
Author(s):  
Miguel A. Arcones
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Limit Distribution ◽  
Linear Regression Model ◽  
Asymptotic Theory ◽  
Multivariate Linear Regression ◽  
Multivariate Linear Regression Model ◽  
Taylor Expansions ◽  
Wide Range ◽  
Different Types

We study the convergence in distribution of M-estimators over a convex kernel. Under convexity, the limit distribution of M-estimators can be obtained under minimal assumptions. We consider the case when the limit is arbitrary, not necessarily normal. If some Taylor expansions hold, the limit distribution is stable. As an application, we examine the limit distribution of M-estimators for the multivariate linear regression model. We obtain the distributional convergence of M-estimators for the multivariate linear regression model for a wide range of sequences of regressors and different types of conditions on the sequence of errors.

scholarly journals Rainfall estimation using Image Processing and Regression model on DWR Rainfall Product for Delhi-NCR Region

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Kuldeep Srivastava ◽  
Ashish Nigam
Keyword(s):  
Image Processing ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Weather Radar ◽  
Least Square ◽  
Rainfall Data ◽  
Doppler Weather Radar ◽  
Rainfall Estimation ◽  
Radar Rainfall

Observed rainfall is a very essential parameter for the analysis of rainfall, day to day weather forecast and its validation. The observed rainfall data is only available from five observatories of IMD; while no rainfall data is available at various important locations in and around Delhi-NCR. However, the 24-hour rainfall data observed by Doppler Weather Radar (DWR) for entire Delhi and surrounding region (up to 150 km) is readily available in a pictorial form. In this paper, efforts have been made to derive/estimate the rainfall at desired locations using DWR hydrological products. Firstly, the rainfall at desired locations has been estimated from the precipitation accumulation product (PAC) of the DWR using image processing in Python language. After this, a linear regression model using the least square method has been developed in R language. Estimated and observed rainfall data of year 2018 (July, August and September) was used to train the model. After this, the model was tested on rainfall data of year 2019 (July, August and September) and validated.With the use of linear regression model, the error in mean rainfall estimation reduced by 46.58% and the error in max rainfall estimation reduced by 84.53% for the year 2019. The error in mean rainfall estimation reduced by 81.36% and the error in max rainfall estimation reduced by 33.81% for the year 2018. Thus, the rainfall can be estimated with a fair degree of accuracy at desired locations within the range of the Doppler Weather Radar using the radar rainfall products and the developed linear regression model.

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.

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