## Electronic Theses and Dissertations

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### Deming Regression: An Alternative to Ordinary Least Squares in Handling Error in Variables Models with Noisy Datasets

#### Document Type

Thesis - University Access Only

2013

#### Degree Name

Master of Science (MS)

#### Department / School

Mathematics and Statistics

Thomas Brandenburger

#### Abstract

The regular regression procedure predicts the value of the dependent variable using the error free independent variable, but in reality, we may always have some degree of measurement error in independent variable, which makes the parameter estimates biased. In these cases, we need to look for an alternative to the regular regression model for the correct prediction of the dependent variable. The alternative to Ordinary Least Square (OLS) could be Reduced Major Axis (RMA) and Grouping method when the error variances of both the independent and dependent variables are not exactly known, whereas, in the situation where the error variances are exactly known, the Deming/Orthogonal regression could be the best alternative to OLS. This paper basically focuses on a brief introduction to the different error models with major emphasis on the application of Deming regression procedure, modeled on the principle of projection of data points to the regression line so that the square of the total distance between data points and the regression line is minimized. The angle of projection of data point to the regression line is given by the ratio of the error variances between the independent and dependent variables. When the assumption that the error variable is fixed is violated, the parameter estimates from the Deming regression are unbiased as compared to the Ordinary Least square (OLS) estimates which gives a more accurate prediction. In this study of prediction of starch concentration in the corn flour using the difference in composition of spectra as an input variable, the data points are 34% closer to Deming line as compared to OLS line. For research in biological sciences where independent variable has noise greater than 10%, prediction made by Deming regression beats the OLS and reduces or eliminates bias. We can consider 10% noise in the independent variable as threshold to switch from OLS to Deming regression.

#### Library of Congress Subject Headings

Regression analysis
Least squares
Errors-in-variables models
Mathematical statistics

#### Description

Includes bibliographical references (leaves 42-44)

application/pdf

72

#### Publisher

South Dakota State University

#### Rights

In Copyright - Educational Use Permitted
http://rightsstatements.org/vocab/InC-EDU/1.0/

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