Explained variation

In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained or residual variation. Following Kent (1983), we use the Fraser information (Fraser 1965) where g ( r ) {displaystyle g(r)} is the probability density of a random variable R {displaystyle R,} , and f ( r ; θ ) {displaystyle f(r; heta ),} with θ ∈ Θ i {displaystyle heta in Theta _{i}} ( i = 0 , 1 {displaystyle i=0,1,} ) are two families of parametric models. Model family 0 is the simpler one, with a restricted parameter space Θ 0 ⊂ Θ 1 {displaystyle Theta _{0}subset Theta _{1}} . Parameters are determined by maximum likelihood estimation,