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Consider developing a regression model in a context where substantive theory is weak. To focus on an extreme case, suppose that in fact there is no relationship between the dependent variable and the explanatory variables. Even so, if there are many explanatory variables, the R2 will be high. If explanatory variables with small t statistics are dropped and the equation refitted, the R2 will stay high and the overall F will become highly significant. This is demonstrated by simulation and by asymptotic calculation.
The American Statistician © 1983 American Statistical Association