Stretching a scatterplot. Changing the units of measurement can greatly alter the appearance of a scatterplot. Return to the fossil data from Example 3:

Femur: 38 56 59 64 74 Humerus: 41 63 70 72 84 Chapter 14 Exercises 305 These measurements are in centimeters. Suppose a deranged scientist measured the femur in meters and the humerus in millimeters. The data would then be Femur: 0.38 0.56 0.59 0.64 0.74 Humerus: 410 630 700 720 840

(a) Draw an x axis extending from 0 to 75 and a y axis extending from 0 to 850.

Plot the original data on these axes. Then plot the new data on the same axes in a different color. The two plots look very different.

(b) Nonetheless, the correlation is exactly the same for the two sets of measurements. Why do you know that this is true without doing any calculations?