This approach is similar to the weighted sum method but instead of
directly using the ratings of similar items it uses an approximation
of the ratings based on regression model. In practice, the
similarities computed using cosine or correlation measures may be
misleading in the sense that two rating vectors may be distant (in
Euclidean sense) yet may have very high similarity. In that case using
the raw ratings of the ``so called'' similar item may result in poor
prediction. The basic idea is to use the same formula as the weighted
sum technique, but instead of using the similar item *N*'s ``raw''
ratings values *R*_{u,N}'s, this model uses their approximated values
*R*_{u,N}^{'} based on a linear regression model. If we denote the
respective vectors of the target item *i* and the similar item *N* by
*R*_{i} and *R*_{N} the linear regression model can be expressed as

The regression model parameters and are determined by going over both of the rating vectors. is the error of the regression model.