The substantively weighted least squares (SWLS) procedure is generalized to apply to a wider range of applications. SWLS is based on simple multivariate linear regression. Linear modeling, regression in particular, has spawned more variations, more versions, and more enhancements than perhaps any other statistical procedure. This chapter generalizes the SWLS procedure by using a series of transformations relating the jackknifed residuals to a common j-shaped tabular distribution. This extension, Generalized Substantively Reweighted Least Squares (GSRLS), allows to develop alpha-level positive outlier identification applicable to a wide range of data-analytic settings. The generalization from SWLS to GSRLS is then the ability to alter the threshold according to a desired size of the outlying group. The chapter presents a simple example from a deliberately small sample using data from an 1854 study on mental health in the fourteen counties of Massachusetts.