(*R*-squared). The coefficient of determination. In regression analysis, the square of the correlation between *Y*
(the forecast variable) and
(the estimated *Y* value based on the set of explanatory variables) is denoted as *R*^{2}. *R*^{2}** **can be interpreted as the proportion of variance in *Y* that can be explained by the explanatory variables. *R*^{2} is appropriate only when examining holdout data (use adjusted *R*^{2} for the calibration data). Some researchers believe that the dangers of *R*^{2 }outweigh its advantages. Montgomery and Morrison (1973) provide a rule of thumb for estimating the calculated *R*^{2}^{ }when the true *R*^{2} is zero: it is *R*^{2} = *v/n,* where *v *is the number of variables and* n* is the number of observations. They showed how to calculate the inflation in *R*^{2} and also presented a table showing sample sizes, number of variables, and different assumptions as to the true *R*^{2}. If you are intent on increasing** ***R*^{2}**,**** **
see “Rules for Cheaters” on the Practitioners
page,. *R*^{2}can be especially misleading for time-series data. Used with caution, *R*^{2} may be useful for diagnostic purposes in some cases, most likely when dealing with cross-sectional data. Even then, however, the correlation coefficient is likely to be a better measure.
- Montgomery, D. & D. Morrison (1973), “A note on
adjusting
*R*^{2},” *Journal of Finance*, 28,
1009-1013.