In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the American black bear (Ursus americanus) 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 that is 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.

Use the results from Problem 20 in Section 4.2 to answer the following questions:
(a) Treating total length as the explanatory variable, x, determine the estimates of ß0 and ß1.
(b) Assuming the residuals are normally distributed, test whether a linear relation exists between total length and weight at the α = 0.05 level of significance.
(c) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true leastsquares regression line.
(d) What is the mean weight of American black bears of length 146.0 cm?

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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