LM fitting

A data set has values y_i, each of which has an associated modelled value f_i (also sometimes referred to as ŷ_i). Here, the values y_i are called the observed values and the modelled values f_i are sometimes called the predicted values.

The "variability" of the data set is measured through different sums of squares:

 the total sum of squares (proportional to the sample variance);

 the regression sum of squares, also called the explained sum of squares.

, the sum of squares of residuals, also called the residual sum of squares.

In the above  is the mean of the observed data:

where n is the number of observations.

The notations  and  should be avoided, since in some texts their meaning is reversed to Residual sum of squares and Explained sum of squares, respectively.

The most general definition of the coefficient of determination is