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Activity Number:
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531
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2009 : 2:00 PM to 3:30 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #303414 |
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Title:
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Model for Fitting Two Lines to Data
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Author(s):
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Penelope M. Ellis*+ and Chris Monico and Clyde Martin
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Companies:
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Texas Tech University and Texas Tech University and Texas Tech University
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Address:
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Department of Mathematics, Lubbock, TX, 79409,
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Keywords:
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linear regression ; geometry ; combinatorics
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Abstract:
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A routine problem is to best fit a line to planar data. However, some data sets are best fit using two or more lines. The problem of choosing the number of lines is ill posed (comparable to determining when the determinant of a large matrix is zero). We determine the pair of lines that best fits a set of planar data. There are at least two approaches to this problem. The first method, a combinatorial one, is to partition the data into two subsets and fit two lines to the data using standard least squares. This results in exponential growth if done naively. The second method, a geometric approach, is based on the manifold of pairs of lines and the minimization of a functional on this manifold. The two methods are equivalent but give different insights. We present algorithms that solve the combinatorial problem in polynomial time and describe in detail the corresponding geometry.
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