Add More Dimensions

What we have covered so far

In the previous two chapters, we predicted output from an input. A restaurant’s pizza sales from its reservations. Most interesting real-world problems, however, have more than one input. Even something as simple as pizza sales is not likely to depend on reservations alone. For example, if there are many tourists in town, the restaurant will probably sell more pizzas, even if it has as many reservations as yesterday.

If pizza sales have many variables, imagine how many variables we’ll have to consider once we get into complex domains, like recognizing pictures. A learning program that only supports one variable will never solve those hairy problems. If we ever want to tackle them, we would better upgrade our program to support multiple input variables.

We can learn from multiple input variables with an advanced version of linear regression called multiple linear regression. In this chapter, we’ll extend our program to support multiple linear regression. We’ll also add a few tricks to our bag, including a couple of useful matrix operations and several NumPy functions. Let’s dive right in!