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Comparison of structural and least-squares lines for estimating geologic relations

Mathematical Geology

By:
and
DOI: 10.1007/BF00890122

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Abstract

Two different goals in fitting straight lines to data are to estimate a "true" linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating "true" straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal-predicting the dependent variable-OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. ?? 1990 International Association for Mathematical Geology.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Comparison of structural and least-squares lines for estimating geologic relations
Series title:
Mathematical Geology
DOI:
10.1007/BF00890122
Volume
22
Issue:
8
Year Published:
1990
Language:
English
Publisher location:
Kluwer Academic Publishers-Plenum Publishers
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Mathematical Geology
First page:
1027
Last page:
1049