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Activity Number:
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313
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #304215 |
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Title:
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Simple Linear Regression When Both Variables Are Random
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Author(s):
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Christopher Tong*+ and Shubing Wang
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Companies:
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Merck & Co., Inc. and Merck & Co., Inc.
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Address:
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RY33-300, Rahway, NJ, 07065,
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Keywords:
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Linear regression ; principal components ; geometric mean regression ; orthogonal distance regression
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Abstract:
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Consider the estimation of a linear relationship between paired measurements from a random sample of subjects. Ordinary least squares (OLS) regression provides two different regression lines, depending on which variable is selected to be the "independent" one. This approach is optimal for predicting one variable conditioned on the value of the other. However here we are concerned with estimating the slope parameter: OLS regression will be biased for our problem. We focus on regression methods that treat both variables symmetrically and thus estimate a single regression line. We re-examine methods considered by Isobe et al. (1990) and Babu & Feigelson (1992). In general, our problem is related to but distinct from the measurement error regression problem, where latent variable models are deployed. Here, simpler models such as the bivariate normal and other elliptical
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