Linear Regression

Abstract

When we first meet Statistics, we encounter random quantities (random variables, in probability language, or variates, in statistical language) one at a time. This suffices for a first course.Soon however we need to handle more than one random quantity at a time. Already we have to think about how they are related to each other. Let us take the simplest case first, of two variables. Consider first the two extreme cases. At one extreme, the two variables may be independent (unrelated). For instance, one might result from laboratory data taken last week, the other might come from old trade statistics. The two are unrelated. Each is uninformative about the other. They are best looked at separately. What we have here are really two one-dimensional problems, rather than one two-dimensional problem, and it is best to consider matters in these terms.