In the abstract, regression is a very simple concept: you want to predict one set of numbers given another set of numbers. For example, actuaries might want to predict how long a person will live given their smoking habits, while meteorologists might want to predict the next day’s temperature given the previous day’s temperature. In general, we’ll call the numbers you’re given inputs and the numbers you want to predict outputs. You’ll also sometimes hear people refer to the inputs as predictors or features.

What makes regression different from classification is that the outputs are really numbers. In classification problems like those we described in Chapter 3, you might use numbers as a dummy code for a categorical distinction so that 0 represents ham and 1 represents spam. But these numbers are just symbols; we’re not exploiting the “numberness” of 0 or 1 when we use dummy variables. In regression, the essential fact about the outputs is that they really are numbers: you want to predict things like temperatures, which could be 50 degrees or 71 degrees. Because you’re predicting numbers, you want to be able to make strong statements about the relationship between the inputs and the outputs: you might want to say, for example, that when the number of packs of cigarettes a person smokes per day doubles, their predicted life span gets cut in half.

The problem, of course, is that wanting to make precise numerical predictions ...

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