Is predicting number of sales a Regression or Classification problem?

Question

I am a Machine Learning beginner who is currently doing Andrew Ng's Machine Learning course on Coursera. In the lecture, he asked a simple question: Would you call the following a classification or regression problem?

You have a large inventory of identical items. You want to predict how many of these items will sell over the next 3 months

I chose classification since I thought we are just predicting will sell (1) or won't sell (0). But he says it is a regression problem since there are thousands of identical items and it is a continuous output. I don't understand how it is a continuous output. Looks to me like a discrete output having thousands of values. Can someone explain this to me?

Answer 1

I don't understand how it is a continuous output. Looks to me like a discrete output having thousands of values.

Well, continuous output here has not the formal mathematical meaning; strictly speaking, you are correct in that your output (some integer value) is discrete, but this is not the point in this context.

The crucial difference that makes this a regression problem and not a classification one is that, in classification, the output is restricted to some (usually few) predefined values/levels; it is easy to see that this is not the case here, since a quantity sold can be in principle any (integer) value, and it makes no sense at all to consider, say, the values 18 and 19 as different classes.

It may also be useful to try to think of classification output as categories which, in general, may have no ordinal relation between them; from such a perspective, a difference between 18 and 19 can be considered the same with the difference between 18 and 856 (they are simply different categories); Intuitively, it should be obvious that, since we are interested in the exact amount sold, these differences are, well, very different between them, and we would very much prefer to mis-predict a "18" as a "19" rather than as a "856"...