Chapter 4.3, Problem 10AYU

Problems 7–12 use the results from Problems 25–30 in Section 4.1 and Problems 17–22 in Section 4.2.

10. American Black Bears Use the results from Problem 28 in Section 4.1 and Problem 20 in Section 4.2 to:

1. a. Compute the coefficient of determination, R².
2. b. Interpret the coefficient of determination.

References

20. American Black Bears (Refer to Problem 28, Section 4.1.) 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 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 data in the next column represent the lengths of 12 American black bears.

Total Length (cm), x	Weight (kg), y
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
Source: www.fieldtripearth.org

1. a. Find the least-squares regression line, treating total length as the explanatory variable and weight as the response variable.
2. b. Interpret the slope and y-intercept, if appropriate.
3. c. Suppose a 149.0-cm bear is captured in the field. Use the least-squares regression line to predict the weight of the bear.
4. d. What is the residual of the 149.0-cm bear? Is this bear’s weight above or below average for a bear of this length?

28. American Black Bears 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
Source: fieldzripearth.org

1. a. Which variable is the explanatory variable based on the goals of the research?
2. b. Draw a scatter diagram of the data.
3. c. Determine the linear correlation coefficient between weight and length.
4. d. Does a linear relation exist between the weight of the bear and its length?