The calculus techniques you learned in part 2 require well-behaved functions to be applicable. For a derivative to exist, a function needs to be sufficiently smooth, and to calculate an exact derivative or integral, you need a function to have a simple formula. For most real-world data, we aren’t so lucky. Due to randomness or measurement error, we rarely come across perfectly smooth functions in the wild. In this chapter, we cover how to take messy data and model it with a simple mathematical function−a task called regression.
I’ll walk you through an example on a real data set, consisting of 740 used cars listed for sale on the website CarGraph.com. These cars are all Toyota Priuses, and they all have mileage and sale price reported. Plotting this data on a scatter plot, figure 14.1 shows that we can see there’s a downward trend in price as mileage increases. This reflects that cars lose value as they are driven. Our goal is to come up with a simple function that describes how the price of a used Prius changes as its mileage increases.
