# Question

The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the ﬁeld). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears.

Total Length (cm) ..... Weight (kg)

139.0 .......... 110

138.0 .......... 60

139.0 .......... 90

120.5 .......... 60

149.0 .......... 85

141.0 .......... 100

141.0 .......... 95

150.0 .......... 85

166.0 .......... 155

151.5 .......... 140

129.5 .......... 105

150.0 .......... 110

(a) Which variable is the explanatory variable based on the goals of the research?

(b) Draw a scatter diagram of the data.

(c) Determine the linear correlation coefﬁcient between weight and height.

(d) Does a linear relation exist between the weight of the bear and its height?

Total Length (cm) ..... Weight (kg)

139.0 .......... 110

138.0 .......... 60

139.0 .......... 90

120.5 .......... 60

149.0 .......... 85

141.0 .......... 100

141.0 .......... 95

150.0 .......... 85

166.0 .......... 155

151.5 .......... 140

129.5 .......... 105

150.0 .......... 110

(a) Which variable is the explanatory variable based on the goals of the research?

(b) Draw a scatter diagram of the data.

(c) Determine the linear correlation coefﬁcient between weight and height.

(d) Does a linear relation exist between the weight of the bear and its height?

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