Assumptions, Limitations, Practical Considerations - Choice of the Number of Variables
Multiple regression is a seductive technique: "plug in" as many predictor variables as you can think of and usually at least a few of them will come out significant. This is because one is capitalizing on chance when simply including as many variables as one can think of as predictors of some other variable of interest. This problem is compounded when, in addition, the number of observations is relatively low. Intuitively, it is clear that one can hardly draw conclusions from an analysis of 100 questionnaire items based on 10 respondents. Most authors recommend that one should have at least 10 to 20 times as many observations (cases, respondents) as one has variables, otherwise the estimates of the regression line are probably very unstable and unlikely to replicate if one were to do the study over.