Abstract
So far, when we have studied a random variable, say Y, we’ve ruled out any effect of other variables. In this chapter, we study a model which accommodates the systematic effect on Y of one other variable, X— the ONLY systematic effect on Y. We think of X as known or under our control. This X is sometimes called the “explanatory” variable in view of its role as a known or controlled “effect” on Y. So Y is the variable in question and X plays the role of input information relevant to Y. Sometimes, Y is described as the “response” to the “factor” X. In itself, X might or might not be a random variable, but from the point of view of the model, X is not random because the model focuses on particular values of X which are known or in some sense controlled. In other words, it’s a model for the conditional distribution of Y given X.
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© 1994 Springer Science+Business Media New York
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Creighton, J.H.C. (1994). Introduction to Simple Linear Regression. In: A First Course in Probability Models and Statistical Inference. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8540-8_7
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DOI: https://doi.org/10.1007/978-1-4419-8540-8_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6431-6
Online ISBN: 978-1-4419-8540-8
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