http://epm.sagepub.com/cgi/reprint/68/3/431
(the link will get you the article if you are on the campus network)
This paper is based on Monte Carlo simulation.
"Unlike the previously mentioned studies, this study is not concerned with finding an accurate value of the squared multiple correlation coefficient or minimizing the shrinkage of the squared multiple correlation coefficient. Instead, this research attends to the task of finding sample regression models that predict similarly to population regression models. More precisely, what sample size is needed to ensure, with a desired amount of accuracy, that the sample regression equation will perform similarly to the population regression equation? These minimum sample sizes were determined by conducting a series of Monte Carlo simulations. This study determines minimum sample sizes for a wide range of population correlation structures." (p. 433)
The chart below shows how recommended sample size varies with R2.
In judgment analysis, we can assume that R2 will be around .7. The tables in this paper suggest that our general guideline of "the number of cases should be at least six times the number of cues" is reasonable. I am a little unclear on how cue intercorrelations factor into their results. They indicate that they did explore different correlation matrices, but I don't see these reflected in their tables.They conclude:
"When utilizing MLR for prediction purposes, any author or researcher who does not take some aspect of the relationship between variables into consideration when making a sample size recommendation will seldom determine an appropriate sample size needed for the study. Also, the number of predictor variables is an important factor in determining the minimum required sample size. Authors and researchers who do not use the number of predictor variables as a determining factor when selecting appropriate sample sizes will probably end up with sample sizes that are too small or too large.
We recommend using the sample sizes presented in this article as a guideline when using multiple regression for predictive purposes. The results of this study are not recommended when using multiple regression for purposes other than prediction. Different applications of multiple regression usually require different minimum sample sizes (Brooks & Barcikowski, 1995, 1996; Casciok et al., 1978; Darlington, 1990; Gross, 1973; Pedhazur, 1997; Tabachnik & Fidell, 2001)." (p. 441)
In other words, if you are interested in estimating R2 or weights, these sample size estimates don't apply. They only indicate that the sample model will predict about as well in the sample as the population model predicts in the population.
