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Francis Galton, a half-cousin of Charles Darwin, is often credited as the founder of regression analysis, a tool he used for studying heredity and the social sciences. R.A. Fisher seems to be responsible for our current focus of treating the X matrix as fixed and known. In this chapter we give a mathematical, rather than subject matter, definition of regression and discuss many of its standard features. We also introduce prediction theory which is based on having X random. We explore prediction theory’s close connection to regression and use it as the basis for defining many standard features of traditional regression.
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