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Transforming Both Sides of a Tree

 

作者: A.C. Atkinson,  

 

期刊: The American Statistician  (Taylor Available online 1994)
卷期: Volume 48, issue 4  

页码: 307-313

 

ISSN:0003-1305

 

年代: 1994

 

DOI:10.1080/00031305.1994.10476088

 

出版商: Taylor & Francis Group

 

关键词: Box–Cox transformation;Cherry trees;Constructed variable;Deletion estimate;Forest mensuration;Regression diagnostics;Transform both sides

 

数据来源: Taylor

 

摘要:

The volume of a tree trunk can be modeled as a cone or cylinder. However, the variance of the observations increases with volume. To obtain variance homogeneity the response can be transformed, which, unfortunately, destroys the geometric relationship. In this article the method of transforming both sides of an equation is applied to model the Minitab tree data and 70 observations on the volume of pine trees. In both examples the logarithmic transformation of both sides of the equation seems appropriate. To determine the effect of individual observations on this conclusion, the constructed variable for transforming both sides of the equation is derived. This variable is used to provide added variable plots for the transformation and in the construction of deletion estimates of the transformation parameter and of the relatedttest. The only statistical technique used is simple regression through the origin. The article concludes with some comments on forest mensuration as a source of statistical problems.

 

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