degrees of freedom, the number of the candidate independent variables from the best fit selected may be smaller than the total number of final model variables, causing the fit to appear better than it is when adjusting the r2 value for the number of degrees of freedom. It is important to consider how many degrees of freedom have been used in the entire model, not just count the number of independent variables in the resulting fit. Models that are created may be over-simplifications of the real models of the data. Such criticisms, based upon limitations of the relationship between a model and procedure and data set used to fit it, are usually addressed by verifying the model on an independent data set, as in the PRESS procedure. Critics regard the procedure as a paradigmatic example of data dredging, intense computation often being an inadequate substitute for subject area expertise. Additionally, the results of stepwise regression are often used incorrectly without adjusting them for the occurrence of model selection. Especially the practice of fitting the final selected model as if no model selection had taken place and reporting of estimates and confidence intervals as if least-squares theory were valid for them, has been described as a scandal. Widespread incorrect usage and the availability of alternatives such as ensemble learning, leaving all variables in the model, or using expert judgement to identify relevant variables have led to calls to totally avoid stepwise model selection. See also Freedman's paradox Logistic regression Least-angle regression Occam's razor Regression validation Lasso (statistics) References Regression variable selection