Data Mining applications have to deal with increasingly large data sets and complexity. Only algorithms which scale linearly with data size are feasible. We present parallel regression algorithms which after a few initial scans of the data compute predictive models for data mining and do not require further access to the data. In addition, we describe various ways of dealing with the complexity (high dimensionality) of the data. Three methods are presented for three different ranges of attribute numbers. They use ideas from the finite element method and are based on penalised least squares fits using sparse grids and additive models for intermediate and very high dimensional data. Computational experiments confirm scalability both with respect to data size and number of processors.