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PARAMETER ESTIMATION IN LINEAR REGRESSION

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Date Issued:
2006
Abstract/Description:
Today increasing amounts of data are available for analysis purposes and often times for resource allocation. One method for analysis is linear regression which utilizes the least squares estimation technique to estimate a model's parameters. This research investigated, from a user's perspective, the ability of linear regression to estimate the parameters' confidence intervals at the usual 95% level for medium sized data sets. A controlled environment using simulation with known data characteristics (clean data, bias and or multicollinearity present) was used to show underlying problems exist with confidence intervals not including the true parameter (even though the variable was selected). The Elder/Pregibon rule was used for variable selection. A comparison of the bootstrap Percentile and BCa confidence interval was made as well as an investigation of adjustments to the usual 95% confidence intervals based on the Bonferroni and Scheffe multiple comparison principles. The results show that linear regression has problems in capturing the true parameters in the confidence intervals for the sample sizes considered, the bootstrap intervals perform no better than linear regression, and the Scheffe method is too wide for any application considered. The Bonferroni adjustment is recommended for larger sample sizes and when the t-value for a selected variable is about 3.35 or higher. For smaller sample sizes all methods show problems with type II errors resulting from confidence intervals being too wide.
Title: PARAMETER ESTIMATION IN LINEAR REGRESSION.
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Name(s): Ollikainen, Kati, Author
Malone, Linda, Committee Chair
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2006
Publisher: University of Central Florida
Language(s): English
Abstract/Description: Today increasing amounts of data are available for analysis purposes and often times for resource allocation. One method for analysis is linear regression which utilizes the least squares estimation technique to estimate a model's parameters. This research investigated, from a user's perspective, the ability of linear regression to estimate the parameters' confidence intervals at the usual 95% level for medium sized data sets. A controlled environment using simulation with known data characteristics (clean data, bias and or multicollinearity present) was used to show underlying problems exist with confidence intervals not including the true parameter (even though the variable was selected). The Elder/Pregibon rule was used for variable selection. A comparison of the bootstrap Percentile and BCa confidence interval was made as well as an investigation of adjustments to the usual 95% confidence intervals based on the Bonferroni and Scheffe multiple comparison principles. The results show that linear regression has problems in capturing the true parameters in the confidence intervals for the sample sizes considered, the bootstrap intervals perform no better than linear regression, and the Scheffe method is too wide for any application considered. The Bonferroni adjustment is recommended for larger sample sizes and when the t-value for a selected variable is about 3.35 or higher. For smaller sample sizes all methods show problems with type II errors resulting from confidence intervals being too wide.
Identifier: CFE0001482 (IID), ucf:47081 (fedora)
Note(s): 2006-12-01
Ph.D.
Engineering and Computer Science, Department of Industrial Engineering and Management Systems
Doctorate
This record was generated from author submitted information.
Subject(s): Multiple Linear Regression
Parameter Estimation
Bootstrap
Coefficient Estimation
Parameter Confidence Interval
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0001482
Restrictions on Access: public
Host Institution: UCF

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