two resulting subtrees. This can be interpreted as minimizing the squared error of a piecewise constant model.

The M5 algorithm proposed by Quinlan [@quinlan1992learning] allows construction of linear models at the leaves of the resulting tree. The splitting of samples at the internal nodes is chosen so as to minimize the standard deviations on the two sub-populations. Effectively the algorithm builds a regression tree based on a piecewise constant model and exchanges these constant models for more powerful linear models at the leaves. As noted in [@landwehr2003logit] due to the similarity in splitting criteria, the CART and M5 algorithms result in similar tree structures. This similarity not withstanding, M5, and its “rational reconstruction” M5$'$ [@wang1997inducing] have been shown to outperform CART in practice [@wang1997inducing; @vogel07scalable].

Similar to the M5, the HTL algorithm [@torgo1997functional], first builds a CART tree and then replaces the models at the nodes. The main difference in this work from the M5 algorithm is that HTL allows for non-linear regressors at the leaves. Yet another approach, SECRET [@dobra2002secret], constructs an artificial classification problem, and shows that there is merit in building the tree structure using a classification tree algorithm and then finally assigning linear regression models to 