No minimum level for r-squared in regression analysis

April 2016
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The deceptively easy-to-interpret measure of R-squared can make it an attractive statistic for evaluating the overall quality of the regression analysis. Indeed, some court decisions have focused on R-squared. In Valentino v. United States Postal Service, the plaintiff’s expert presented a regression model that had an R-squared value of 0.28 (or 28 percent). The court deemed the regression to have no probative value reasoning that the “low” R-squared value meant that potentially relevant explanatory variables had been omitted. Similarly, in Griffin v. Board of Regents, the court held that “the explanatory power of a model is a factor that may legitimately be considered by the district court in deciding whether the model may be relied upon.”[4] Although there are other cases where a low R-squared statistic did not disqualify a model, an R-squared that is viewed as low may present an additional method for challenging the validity or reliability of a regression analysis.[5]

A common question is whether there is indeed a minimum acceptable value for R-squared. Does an R-squared value need to be greater than a certain arbitrary level (often 50 percent or greater)? AlixPartners'  William Choi, Pablo Florian, and Stuart Miller discuss.

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