Keywords

Multiple Linear Regression, Parameter Estimation, Bootstrap, Coefficient Estimation, Parameter Confidence Interval

Abstract

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.

Notes

If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu

Graduation Date

2006

Semester

Fall

Advisor

Malone, Linda

Degree

Doctor of Philosophy (Ph.D.)

College

College of Engineering and Computer Science

Department

Industrial Engineering and Management Systems

Degree Program

Industrial Engineering and Management Systems

Format

application/pdf

Identifier

CFE0001482

URL

http://purl.fcla.edu/fcla/etd/CFE0001482

Language

English

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Download

Included in

Engineering Commons

Share

COinS