What question did this study set out to answer?

To identify common pitfalls in interpreting the coefficient of determination (R squared) and present a new resistant goodness-of-fit statistic.

November 1, 1985The American Statistician

Cautionary Note aboutR2

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Authors

TKTarald O. KvålsethUniversity of Minnesota

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Implication

Methodological analysis reveals widespread misuse and non-equivalence of alternative R-squared statistics across non-standard regression models, highlighting the need for robust fit measures.

Key Points

To identify common pitfalls in interpreting the coefficient of determination (R squared) and present a new resistant goodness-of-fit statistic.
Analyzed the mathematical equivalence of multiple R-squared definitions in regression models with and without an intercept term.
Demonstrated the practical discrepancies and vulnerabilities of standard formulas using empirical datasets.
Developed an alternative resistant statistic to improve goodness-of-fit evaluation.
Alternative definitions of R squared diverge and are not equivalent outside of standard linear models fitted with an intercept term.
Empirical applications demonstrate that misapplying standard R-squared equations across non-standard regressions yields severely distorted assessments of model fit.
A newly introduced resistant statistic provides a more stable and reliable alternative in the presence of non-standard model structures or outliers.

Cite This Study

Tarald O. Kvålseth (1985) studied this question.

synapsesocial.com/papers/69dab2c2615cc0c8eaa3cde9 https://doi.org/10.1080/00031305.1985.10479448

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Implication

Methodological analysis reveals widespread misuse and non-equivalence of alternative R-squared statistics across non-standard regression models, highlighting the need for robust fit measures.

Cautionary Note aboutR2

Discussion

Member takes

Implication

Key Points

Cite This Study

Cautionary Note aboutR2

Discussion

Member takes

Implication

Key Points

Cite This Study

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