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Regression as parameter prediction is a broad concept that covers everything from predicting house prices, to predicting resource consumption or predicting how much weight concrete can carry. In short, everything where you can put something in a box, or mathematically speaking, all that is continuous.
Classification as parameter prediction is a broad concept that covers everything from suggestion algorithms which are seen at online shops, to diagnosing patients for the healthcare sector. In short, everything where you can put something in a box, or mathematically speaking, everything is discreet.