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Machine learning techniques offer a precious tool box for use withinastronomy to solve problems involving so-called big data. They provide a meansto make accurate predictions about a particular system without prior knowledgeof the underlying physical processes of the data. In this article, and thecompanion papers of this series, we present the set of Generalized LinearModels (GLMs) as a fast alternative method for tackling general astronomicalproblems, including the ones related to the machine learning paradigm. Todemonstrate the applicability of GLMs to inherently positive and continuousphysical observables, we explore their use in estimating the photometricredshifts of galaxies from their multi-wavelength photometry. Using the gammafamily with a log link function we predict redshifts from the PHoto-z AccuracyTesting simulated catalogue and a subset of the Sloan Digital Sky Survey fromData Release 10. We obtain fits that result in catastrophic outlier rates aslow as ~1% for simulated and ~2% for real data. Moreover, we can easily obtainsuch levels of precision within a matter of seconds on a normal desktopcomputer and with training sets that contain merely thousands of galaxies. Oursoftware is made publicly available as an user-friendly package developed inPython, R and via an interactive web application(https://cosmostatisticsinitiative.shinyapps.io/CosmoPhotoz). This softwareallows users to apply a set of GLMs to their own photometric catalogues andgenerates publication quality plots with minimum effort from the user. Byfacilitating their ease of use to the astronomical community, this paper seriesaims to make GLMs widely known and to encourage their implementation in futurelarge-scale projects, such as the Large Synoptic Survey Telescope.

The Overlooked Potential of Generalized Linear Models in Astronomy-II: Gamma regression and photometric redshifts