Multiple Linear Regression

We have already covered regular linear regression, as well as linear regression with polynomial and other terms, and considered training them with both the least squares method and gradient descent. This section of the chapter considers an additional type of linear regression: multiple linear regression, where more than one variable (or feature) is used to construct the model. In fact, we have already used multiple linear regression without calling it as such—when we added dummy variables, and again when we added the sine and cosine terms, we were fitting multiple x variables to predict the single y variable.

Let's consider a simple example of where multiple linear regression naturally arises as a modeling solution. Suppose you were shown the following chart, which is the total annual earnings of a hypothetical tech worker over a long career. You can see that over time, their pay increased, but there are some odd jumps and changes in the data...