Open Access Open Access  Restricted Access Subscription or Fee Access

Impact of Data Structure on the Estimators R-Square and Adjusted R-Square in Linear Regression

A. Y. J. Akossou, R palm


The effects of the data structure on the quality of the estimator R-square and adjusted R-square in linear multiple regression was evaluated by Monte Carlo simulation. A total of 216 data were generated through which the number of variables, the theoretical value of R-square value, the colinearity between the explanatory variables and the index of coefficient decrease which measures the importance of the explanatory variables in the model were controlled. The results confirmed that R-square is a biased estimator. If much of users are conscious that the estimator R^2 is biased, they consider that the estimator R-square_a is unbiased, or at least that its bias is negligible. This study however revealed that, in unfavourable situations (small theoretical values R-square_0 and small sample size compared to the number of explanatory variables) bias can be significant when the model is established by using selection procedure. The user’s attention is drawn to the risks incurred in the use of this parameter.


Linear regression, R-square, adjusted R-square, data structure, simulation.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.