Saturated Models, Deviance and the Derivation of Sum of Squares

Before we discuss deviance, we first need to understand what the Saturated, Proposed and Null Models are. A Saturated Model is where the number of parameters/coefficients is equal to the number of data points. This is like a'connect the dots' model where the line or curve passes through each point. This is considered to be the perfect model as it takes into account all the variance in the data and has the maximum achievable likelihood. A Null Model is the opposite with only one parameter, which is the intercept.