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American Black Bears(Refer to Black Bears The American
Chapter 3, Problem 20AYU(choose chapter or problem)
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 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.
\(\begin{array}{|c|c|} \hline \text { Total Length }(\mathrm{cm}) & \text { Weight (kg) } \\ \hline 139.0 & 110 \\ \hline 138.0 & 60 \\ \hline 139.0 & 90 \\ \hline 120.5 & 60 \\ \hline 149.0 & 85 \\ \hline 141.0 & 100 \\ \hline 141.0 & 95 \\ \hline 150.0 & 85 \\ \hline 166.0 & 155 \\ \hline 151.5 & 140 \\ \hline 129.5 & 105 \\ \hline \end{array}\)
Source: www.fieldtripearth.org
(a) Find the least-squares regression line, treating total length as the explanatory variable and weight as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(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.
(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?
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QUESTION:
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 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.
\(\begin{array}{|c|c|} \hline \text { Total Length }(\mathrm{cm}) & \text { Weight (kg) } \\ \hline 139.0 & 110 \\ \hline 138.0 & 60 \\ \hline 139.0 & 90 \\ \hline 120.5 & 60 \\ \hline 149.0 & 85 \\ \hline 141.0 & 100 \\ \hline 141.0 & 95 \\ \hline 150.0 & 85 \\ \hline 166.0 & 155 \\ \hline 151.5 & 140 \\ \hline 129.5 & 105 \\ \hline \end{array}\)
Source: www.fieldtripearth.org
(a) Find the least-squares regression line, treating total length as the explanatory variable and weight as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(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.
(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?
ANSWER:Step 1 of 5
a). The least-squares regression line treating total length as the explanatory variable and weight as the response variable is calculated by using excel.
Enter the data in a Excel sheet
Go Data select data Analysis regression then ok
Enter the X and Y range and output range and Select Residuals
OK
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