The chapter explores a series of extensionsMultiple regression to the regression model considered in earlier chapters. Section 8.1 introduces the use of prior knowledge in regression analysis, including the construction of prior distributions from fictitious observations. In Sect. 8.2 Bayesian regression is combined with the FSFS. Section 8.3 provides analyses of successive annual sets of trade data, in which the prior distribution is updated annually. Heteroskedastic regression is introduced in Sect. 8.4. The analysis of trade data makes clear the importance of avoiding models in which the variance goes to zero as x does. Section 8.5 extends the analysis of trade data to data from several regression hyperplanes. The number of groups is estimated in Sect. 8.5.2 from an FSFS which starts the search many times from random points. Regression clustering (Sect. 8.5.3) involves the choice of parameters and, for robustnessRobustness, a choice of trimming level. The monitoring approach in Sect. 8.5.4 identifies solutions which do not depend on arbitrary choices of these hyper-parameters. The fourth extension, in Sect. 8.6, is to use monitoring to provide tools for modelling short-term economic time series that may have trends, time varying seasonality, and level shiftsLevel shifts. The two final extensions, in Sects. 8.7 and 8.8 are to regression in which the explanatory variables are the components of a composition and to censored regression data.