 Notes About the Last Principal ComponentWorking Papers from Ecole des Hautes Etudes Commerciales, Universite de Geneve- Abstract: This article gives results specifically related to the last principal component. This linear combination of variables plays an important role when one tries to fit a hyperplane to a cloud of points. In data analysis, variables are often subject to a linear transformation. The results that we provide here take account of such a transformation. Firstly, we define a "distance" between a variable and a set U of variables. Among the linear combinations of the variables in U, the last principal component is the most "distant" from U. Secondly, we clarify the link between the last principal component and (i) linear dependence, (ii) equation of an optimal hyperplane, and (iii) invariance of the optimal hyperplane under linear transformation of the variables. Finally, we show how the decomposition formula of inertia of a hyperplane in principal components analysis and the decomposition formula of the total sum of squares in linear regression both derive from a common principle. Keywords: DATA ANALYSIS; MODELS; MATHEMATICS (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:fth:ehecge:2000.16 Access Statistics for this paper More papers in Working Papers from Ecole des Hautes Etudes Commerciales, Universite de Geneve- Suisse; Ecole des Hautes Etudes Commerciales, Universite de Geneve, faculte des SES. 102 Bb. Carl-Vogt CH - 1211 Geneve 4, Suisse. Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.