Comparing models using the extra sum-of squares F test

Abstract When you compare two nested models, the model with more parameters will almost always fit the data better (have a lower sum-of-squares) than the model with fewer parameters. It is not enough to compare sum-of-squares. We need to use a statistical approach to decide which model to accept. As its name suggests, the extra sum-of-squares F test is based on the difference between the sum-of-squares of the two models. It also takes into account the number of data points and the number of parameters of each model. It uses this information to compute an F ratio, from which it calculates a P value.