(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 R².  R² can be interpreted as the proportion of variance in Y that can be explained by the explanatory variables. R² is appropriate only when examining holdout data (use adjusted R² for the calibration data). Some researchers believe that the dangers of R² outweigh its advantages. Montgomery and Morrison (1973) provide a rule of thumb for estimating the calculated R² when the true R² is zero: it is R² = v/n, where v is the number of variables and n is the number of observations. They showed how to calculate the inflation in R² and also presented a table showing sample sizes, number of variables, and different assumptions as to the true R². If you are intent on increasing R², see “Rules for Cheaters” on the Practitioners page,. R²can be especially misleading for time-series data. Used with caution, R² 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 R²,” Journal of Finance, 28, 1009-1013.