Exact Distributions of <i>R²</i> and Adjusted <i>R²</i> in a Linear Regression Model with Multivariate <i>t</i> Error Terms

• Ohtani Kazuhiro

  Graduate School of Economics, Kobe University

• Tanizaki Hisashi

  Graduate School of Economics, Kobe University

Bibliographic Information

Other Title

• Exact Distributions of R2 and Adjusted R2 in a Linear Regression Model with Multivariate t Error Terms

Abstract

In this paper we consider a linear regression model when error terms obey a multivariate t distribution, and examine the effects of departure from normality of error terms on the exact distributions of the coefficient of determination (say, R²) and adjusted R² (say, R²). We derive the exact formulas for the density function, distribution function and m-th moment, and perform numerical analysis based on the exact formulas. It is shown that the upward bias of R² gets serious and the standard error of R² gets large as the degrees of freedom of the multivariate t error distribution (say, ν₀) get small. The confidence intervals of R² and R² are examined, and it is shown that when the values of ν₀ and the parent coefficient of determination (say, Φ) are small, the upper confidence limits are very large, relative to the value of Φ.

Journal

• JOURNAL OF THE JAPAN STATISTICAL SOCIETY

  JOURNAL OF THE JAPAN STATISTICAL SOCIETY 34 (1), 101-109, 2004

  THE JAPAN STATISTICAL SOCIETY

Keywords

• adjusted <i>R²</i>
• exact distribution
• interval estimation
• multivariate <i>t</i> error terms
• <i>R²</i>

Details

• CRID: 1390282680262172160
• NII Article ID: 110003144475
• NII Book ID: AA1105098X
• DOI: 10.14490/jjss.34.101
• ISSN: 13486365
• ISSN: 18822754
• MRID: 2084063
• NDL BIB ID: 7042932
• Web Site: http://id.ndl.go.jp/bib/7042932
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7042932
• Web Site: https://www.jstage.jst.go.jp/article/jjss/34/1/34_1_101/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed