What question did this study set out to answer?

Investigate the behavior of standard goodness-of-fit statistics when screening out statistically insignificant predictor variables in regression equations where no true relationship exists.

May 1, 1983The American Statistician

A Note on Screening Regression Equations

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Authors

DFDavid A. FreedmanTulane University

Discussion

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Implication

Methodological study demonstrates spurious significance in regression models with screened predictors, highlighting the risk of false-positive associations when theory is absent.

Key Points

Investigate the behavior of standard goodness-of-fit statistics when screening out statistically insignificant predictor variables in regression equations where no true relationship exists.
Analyzed the extreme scenario where an outcome variable has zero true statistical relationship with a large pool of explanatory variables.
Implemented a two-step screening procedure that drops explanatory variables with small t-statistics and refits the reduced regression equation.
Evaluated the properties of R-squared and the overall F-statistic using mathematical asymptotic calculations and simulations.
Demonstrated that initial regression models containing many explanatory variables yield elevated R-squared values purely by chance.
Showed that dropping variables with small t-statistics and refitting retains high R-squared values while causing the overall F-statistic to become highly significant despite the complete absence of true underlying effects.

Cite This Study

David A. Freedman (1983) studied this question.

synapsesocial.com/papers/69d8a61ed2f7327e70ae3cf4 https://doi.org/10.1080/00031305.1983.10482729

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May 1, 1983The American Statistician

A Note on Screening Regression Equations

View Full Paper

Ask AI

Bookmark

Authors

DFDavid A. FreedmanTulane University

Discussion

Member takes

Implication

Methodological study demonstrates spurious significance in regression models with screened predictors, highlighting the risk of false-positive associations when theory is absent.

Key Points

Investigate the behavior of standard goodness-of-fit statistics when screening out statistically insignificant predictor variables in regression equations where no true relationship exists.
Analyzed the extreme scenario where an outcome variable has zero true statistical relationship with a large pool of explanatory variables.
Implemented a two-step screening procedure that drops explanatory variables with small t-statistics and refits the reduced regression equation.
Evaluated the properties of R-squared and the overall F-statistic using mathematical asymptotic calculations and simulations.
Demonstrated that initial regression models containing many explanatory variables yield elevated R-squared values purely by chance.
Showed that dropping variables with small t-statistics and refitting retains high R-squared values while causing the overall F-statistic to become highly significant despite the complete absence of true underlying effects.

Cite This Study

David A. Freedman (1983) studied this question.

synapsesocial.com/papers/69d8a61ed2f7327e70ae3cf4 https://doi.org/10.1080/00031305.1983.10482729

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