The determination of relationships between measurements of various parts of a particular organism is a topic of interest in the branch of biology called allometry.* Suppose a biologist observes that the shoulder height h and antler size w of an elk, both in centimeters (cm), are related as indicated in this table:

a. For each data point (h, w) in the table, plot the point (ln h, ln w) on a graph. Note that the scatter diagram suggests that y = ln w and x = ln h are linearly related.

b. Find the least-squares line y = mx + b for the data (ln h, ln w) you obtained in part (a).

c. Find numbers a and c so that w = ah^c.

Transcribed Image Text:

Shoulder Height h (cm) 87.9 95.3 106.7 115.4 127.2 135.8 Antler Size w (cm) 52.4 60.3 73.1 83.7 98.0 110.2