A note on adjusting

• Main Authors: MONTGOMERY, David B., Morrison, D.G.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 1973
• Subjects: Business
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/1601; https://ink.library.smu.edu.sg/context/lkcsb_research/article/2600/viewcontent/A_Note_on_Adjusting__mathrmR_sup_2__sup_.pdf
• Institution: Singapore Management University

Whenever a regression analysis is run, one of the key statistics which is reported is the coefficient of determination or, as it is more commonly kn R2. This quantity represents the proportion of the variance of the dependent variable that is associated with ("explained by") the set of independent vari- ables. However, this statistic is a biased estimate of the true coefficient of determination for the underlying population. Moreover, the bias in unadjusted R2 can be sizeable and may lead to serious misinterpretation of research results. The purpose of this note is to examine the magnitude of the bias in R2 and to discuss some of the properties of R2 adjusted for degrees of freedom, a statistic which is less biased than R2. The properties of the unadjusted R2 are examined in the first part of this note. The second part describes the properties of adjusted R2 when adjustment is considered necessary.