Best Probable Subset: A New Method for Reducing Data Dimensionality in Linear Regression

Authors

Elieser Nodarse, Florida International UniversityFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

Hassan Zahedi

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Sneh Gulati

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Golam Kibria

Third Advisor's Committee Title

Committee Member

Fourth Advisor's Name

Zhenmin Chen

Fourth Advisor's Committee Title

Committee Member

Keywords

Linear Regression, Subset Selection, forward selection, backward elimination, regression trees, random forest, best subset selection, high dimensional data, regression

Date of Defense

4-11-2019

Abstract

Regression is a statistical technique for modeling the relationship between a dependent variable Y and two or more predictor variables, also known as regressors. In the broad field of regression, there exists a special case in which the relationship between the dependent variable and the regressor(s) is linear. This is known as linear regression.

The purpose of this paper is to create a useful method that effectively selects a subset of regressors when dealing with high dimensional data and/or collinearity in linear regression. As the name depicts it, high dimensional data occurs when the number of predictor variables is far too large to use commonly known methods. Collinearity, on the other hand, occurs when there exists a linear relationship amongst one or more pairs of independent variables.

This paper is divided into three main section: an introduction, which reviews key concepts that are needed for a full understanding of the paper; the methodology, which guides the reader, step-by-step, through the process of the newly devised method; results, which thoroughly explain and analyze any findings and propose further ideas to be studied.

Identifier

FIDC007704

Recommended Citation

Nodarse, Elieser, "Best Probable Subset: A New Method for Reducing Data Dimensionality in Linear Regression" (2019). FIU Electronic Theses and Dissertations. 4280.
https://digitalcommons.fiu.edu/etd/4280