Linear models

A small baking outfit in upstate New York called No Scone Unturned keeps careful records of the baked goods it produces. The left panel of Figure 9.1 is a scatterplot of diameters and circumferences (in centimeters) of No Scone Unturned's cookies, and depicts their relationship:

Figure 9.1: A scatterplot of diameters and circumferences of No Scone Unturned's cookies (left); the same plot with a best fit regression line plotted over the data points (right)

A straight line is the perfect thing to represent this data. After fitting a straight line to the data, we can make predictions about the circumferences of cookies that we haven't observed, such as 11 or 0.7 (if you weren't playing truant in grade school, you'd know there's a consistent and predictable relationship between the diameter of a circle and the circle's circumference, namely π, but we'll ignore that for now).

You may have learned that the equation that describes a line in a Cartesian plane is:

b is the y-intercept ...