Example 15.1

EXAMPLE 1 Fossil bones

In Examples 3 and 4 in Chapter 14, we saw that the lengths of two bones in fossils of the extinct beast archaeopteryx closely follow a straight-line pattern. Figure 15.1 plots the lengths for the five available fossils. The regression line on the plot gives a quick summary of the overall pattern.

Figure 15.1: Figure 15.1 Using a straight-line pattern for prediction, Example 1. The data are the lengths of two bones in five fossils of the extinct beast archaeopteryx.

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Another archaeopteryx fossil is incomplete. Its femur is 50 centimeters long, but the humerus is missing. Can we predict how long the humerus is? The straight-line pattern connecting humerus length to femur length is so strong that we feel quite safe in using femur length to predict humerus length. Figure 15.1 shows how: starting at the femur length (50 cm), go up to the line, then over to the humerus length axis. We predict a length of about 56 cm. This is the length the humerus would have if this fossil’s point lay exactly on the line. All the other points are close to the line, so we think the missing point would also be close to the line. That is, we think this prediction will be quite accurate.