In machine learning, classification and regression problems are two main types of supervised learning tasks. The main difference between them is the type of output variable they predict.
In a classification problem, the output variable is categorical or discrete, meaning it belongs to a specific class or category. The goal of a classification model is to determine the class to which a given input instance belongs to. The input data could be anything from an image, speech, text or a set of numeric features.
For example, a loan provider could use a classification model to predict whether an applicant is likely to default on a loan or not. The classes here are "default" or "non-default". Another example is a spam classifier that determines whether an email is "spam" or "not spam".
On the other hand, regression problems involve predicting a continuous numerical output variable based on a set of input features. The output variable could be anything from a temperature, distance, time to completion, or stock price.
For example, a retailer could use a regression model to predict the amount of sales in dollars based on the store’s location, weather, day of the week, and other input features. It could also be used to predict the price of a house based on factors such as the number of bedrooms, square footage, and location.
In summary, classification and regression problems differ in their output variable. Classification predicts a categorical variable whereas regression predicts a continuous numerical variable.