This thesis presents a method of model selection which uses simulation to choose between models containing different numbers of parameters. This method is applied to the problem of choosing between a simple linear or a two-phase linear model, using either ordinary least squares regression or reduced major axis regression, to fit two-phase models which are continuous or discontinuous at the change point. The literature and commonly used software packages use only ordinary least squares regression to fit piecewise linear models. Thus, the method presented here makes a contribution to the field. The method is applied to simulated data and also to empirical data sets.