Errors in Variables: A Problem in Regression and its Solution

1986 ◽  
Vol 18 (5) ◽  
pp. 687-693 ◽  
Author(s):  
K J Thomson ◽  
K G Willis
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Car Ownership ◽  
Errors In Variables ◽  
Socioeconomic Analysis ◽  
Multiple Regression Models ◽  
Least Squares Techniques

It is not uncommon in socioeconomic analysis to measure variables with error, as in a 10% census. The estimation of linear regression coefficients using such ‘errors-in-variables’ models requires modification of the usual ordinary least squares techniques. The underlying theory both for simple and for multiple regression models is explained, and followed up with a numerical example based on a structure plan model of car ownership.

scholarly journals A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

2018 ◽  
pp. 1-8
Author(s):  
Warha, Abdulhamid Audu ◽  
Yusuf Abbakar Muhammad ◽  
Akeyede, Imam
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Linear Regression Models ◽  
Independent Variables ◽  
Different Levels

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

scholarly journals How cann soccer improve statistical learning?

2014 ◽  
Vol 2 (7) ◽  
pp. 83-87
Author(s):  
Enivaldo C. Rocha ◽  
Dalson Britto Figueiredo Filho ◽  
Ranulfo Paranhos ◽  
José Alexandre Silva Jr. ◽  
Denisson Silva
Keyword(s):  
Linear Regression ◽  
Statistical Learning ◽  
Undergraduate Students ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Practical Application ◽  
Implementation Cost ◽  
Home Team ◽  
Classical Hypothesis

This paper presents an active classroom exercise focusing on the interpretation of ordinary least squares regression coefficients. Methodologically, undergraduate students analyze Brazilian soccer data, formulate and test classical hypothesis regarding home team advantage. Technically, our framework is simply adapted for others sports and has no implementation cost. In addition, the exercise is easily conducted by the instructor and highly enjoyable for the students. The intuitive approach also facilitates the understanding of linear regression practical application.

scholarly journals New Algorithms for L1 Norm Regression

2019 ◽  
Vol 1 (1) ◽  
pp. 1-18
Author(s):  
Bijan Bidabad
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Simple Linear Regression ◽  
L1 Norm ◽  
Median Problem ◽  
Regression Parameters ◽  
Multiple Regression Models ◽  
Weighted Median ◽  
Weighted Median Problem ◽  
New Algorithms

In this paper, we propose four algorithms for L1 norm computation of regression parameters, where two of them are more efficient for simple and multiple regression models.  However, we start with restricted simple linear regression and corresponding derivation and computation of the weighted median problem. In this respect, a computing function is coded.  With discussion on the m parameters model, we continue to expand the algorithm to include unrestricted simple linear regression, and two crude and efficient algorithms are proposed. The procedures are then generalized to the m parameters model by presenting two new algorithms, where the algorithm 4 is selected as more efficient. Various properties of these algorithms are discussed.

Robust Weighted Least Squares Estimation of Regression Parameter in the Presence of Outliers and Heteroscedastic Errors

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Bello Abdulkadir Rasheed ◽  
Robiah Adnan ◽  
Seyed Ehsan Saffari ◽  
Kafi Dano Pati
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Robust Regression ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Model Parameters ◽  
Constant Variance ◽  
Regression Parameters ◽  
M Estimation

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

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