The Relationship of Corrected R‑Squared and the Incremental t‑Statistic

The use of corrected [R] squared in incremental [t]-statistics as a criterion for stopping a stepwise regression program is questioned. This Note argues that such use is equivalent to including those variables whose incremental [t]-statistic is greater than one in absolute value; that is, including variables whose estimated coefficient exceeds the estimated standard error in absolute value. Thus there appears little or no need for regression packages to output corrected [R] squared. It is also stated that uncorrected [R] squared is a better estimator of the population squared multiple correlation coefficient. (October 1969)