Mean and variance of \(R^ 2\) in small and moderate samples
type: Item
instance of: scholarly article
title: Mean and variance of \(R^ 2\) in small and moderate samples
zbMATH Open document ID: 0617.62117
DOI: 10.1016/0304-4076(87)90027-3
published in: Journal of Econometrics
publication date: 1987-01-01T00:00:00Z
review text: We derive and use easily computable expressions for the mean and variance of \(R^ 2\) in the standard linear regression model with fixed regressors. In respect to its probability limit \(R^ 2\) is seriously biased upward in small samples; the 'adjusted' \(\bar R{}^ 2\) does much better. But at sample sizes where these distinctions matter both measures are thoroughly unreliable because of their large dispersion. \(R^ 2\) should not be quoted for samples of less than fifty observations.
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 4001284
zbMATH Keywords: small sample properties
zbMATH Keywords: R square statistic
zbMATH Keywords: adjusted R square
zbMATH Keywords: measures of goodness of fit
zbMATH Keywords: upward bias
zbMATH Keywords: mean
zbMATH Keywords: variance
Wikidata QID: Q60016595
author: Jan S. Cramer
MaRDI profile type: Publication
full work available at URL: 0304-4076(87)90027-3
OpenAlex ID: W2075007695
cites work: The Selection of Variates for Use in Prediction with Some Comments on the General Problem of Nuisance Parameters
cites work: Q5615180
cites work: Posterior distribution for the multiple correlation coefficient with fixed regressors
cites work: Q5609894
cites work: Q5515568
cites work: Q5626055
description: scientific article; zbMATH DE number 4001284