Regression analysis : a geometric approach
Regression analysis is traditionally presented in algebraic equations and matrices. However, it can also be discussed in a geometric framework. Previous studies have shown that the key concepts in regression analysis, including method of least squares, regression coefficients, simple and partial cor...
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| 格式: | Theses and Dissertations |
| 出版: |
2008
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| 在線閱讀: | http://hdl.handle.net/10356/7748 |
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| 機構: | Nanyang Technological University |
| 總結: | Regression analysis is traditionally presented in algebraic equations and matrices. However, it can also be discussed in a geometric framework. Previous studies have shown that the key concepts in regression analysis, including method of least squares, regression coefficients, simple and partial correlation coefficients, have direct visual analogues in geometry. In this paper, we not only summarize the previous findings mentioned above, but also use geometry to prove the Frisch-Waugh-Lovell Theorem completely and hence give another four geometric expressions of regression coefficients. In addition, we find another geometric interpretation of partial correlation coefficients and prove three formulas that display the relationships among simple, multiple and partial correlation coefficients. |
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