[EX03-98] Wildlife populations are monitored with aerial photographs. The number of animals and their locations relative to areas inhabited by the human population are useful information.

Sometimes it is possible to monitor the physical characteristics of the animals. The length of an alligator can be estimated quite accurately from aerial photographs, but its weight cannot. The following data are the lengths, x (in inches), and weights, y (in pounds), of alligators captured in central Florida and can be used to predict the weight of an alligator based on its length.

Weight Length Weight Length Weight Length 130 94 38 72 44 61 51 74 366 128 106 90 640 147 84 85 84 89 28 58 80 82 39 68 80 86 83 86 42 76 110 94 70 88 197 114 33 63 61 72 102 90 90 86 54 74 57 78 36 69 Source: http://exploringdata.cqu.edu.au/stories.htm alligatr

a. Construct a scatter diagram for length, x, and weight, y.

b. Does it appear that the weight of an alligator is predictable from its length? Explain.

c. Is the relationship linear?

d. Explain why the line of best fit, as described in this chapter, is not adequate for estimating weight based on length.

e. Find the value of the linear correlation coefficient.

f. Explain why the value of r can be so high for a set of data that is so obviously not linear in nature.