choices of pseudo-R2. One is the generalized R2 originally proposed by Cox & Snell, and independently by Magee: where is the likelihood of the model with only the intercept, is the likelihood of the estimated model (i.e., the model with a given set of parameter estimates) and n is the sample size. It is easily rewritten to: where D is the test statistic of the likelihood ratio test. Nico Nagelkerke, noted that it had the following properties: It is consistent with the classical coefficient of determination when both can be computed; Its value is maximised by the maximum likelihood estimation of a model; It is asymptotically independent of the sample size; The interpretation is the proportion of the variation explained by the model; The values are between 0 and 1, with 0 denoting that model does not explain any variation and 1 denoting that it perfectly explains the observed variation; It does not have any unit. However, in the case of a logistic model, where cannot be greater than 1, R2 is between 0 and : thus, Nagelkerke suggested the possibility to define a scaled R2 as R2/R2max. Comparison with norm of residuals Occasionally, the norm of residuals is used for indicating goodness of fit. This term is calculated as the square-root of the sum of squares of residuals: Both R2 and the norm of residuals have their relative merits. For least squares analysis R2 varies between 0 and 1, with larger numbers indicating better fits and 1 representing a perfect fit. The norm of residuals varies from 0 to infinity with smaller numbers indicating better fits and zero indicating a perfect fit. One advantage and disadvantage of R2 is the term acts to normalize the value. If the yi values are all multiplied by a constant, the norm of residuals will also change by that constant but R2 will stay the same. As a basic example, for the linear least squares fit to the set of data: R2 = 0.998, and norm of residuals = 0.302. If all values of y are multiplied by 1000 (for example, in an SI prefix change), then R2 remains the same, but norm of residuals = 302. Another single-parameter indicator of fit is the RMSE of the residuals, or standard deviation of the residuals. This would have a value of 0.135 for the above example given that the fit was linear with an