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Chapter 12: Q.39 (page 814)

Brawn versus brain How is the weight of an animal鈥檚 brain related to the weight of its body? Researchers collected data on the brain weight (in grams) and body weight (in Page Number: 813 Page Number: 814 kilograms) for 96species of mammals. The following figure is a scatterplot of the logarithm of brain weight against the logarithm of body weight for all 96species. The least-squares regression line for the transformed data is

logy鈭�=1.01+0.72logxlogy^=1.01+0.72logx

Based on footprints and some other sketchy evidence, some people believe that a large ape-like animal, called Sasquatch or Bigfoot, lives in the Pacific Northwest. Bigfoot鈥檚 weight is estimated to be about 127kilograms (kg). How big do you expect Bigfoot鈥檚 brain to be?

Short Answer

Expert verified

The expected brain weight is 334.734grams.

Step by step solution

01

Given Information

Given data:

02

Explanation

Substituting the value of xin the regression equation

logy=1.01+0.72log(127)

=2.5247

Taking each side of the result's exponential with a base of 10:

y=10logy

=102.5247

=334.734

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Most popular questions from this chapter

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=foot length and y=height were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is the equation of the least-squares regression line for predicting height from foot length?

a. height^=10.2204+0.4117(foot length) height^=10.2204+0.4117(foot length)

b.height^=0.4117+3.0867 (foot length) height^=0.4117+3.0867(foot length)

c. height^=91.9766+3.0867(foot length) height^=91.9766+3.0867(foot length)

d. height^=91.9766+6.47044 (foot length)height^=91.9766+6.47044(foot length)

e. height^=3.0867+6.47044(foot length)heiight^=3.0867+6.47044(foot length)

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a. Here is some computer output and a residual plot from a least-squares regression on these data. Explain why a linear model may not be appropriate in this case.

The foresters are considering two possible transformations of the original data: (1) cubing the diameter values or (2) taking the natural logarithm of the yield measurements. After transforming the data, a least-squares regression analysis is performed. Here is some computer output and a residual plot for each of the two possible regression models:

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Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightwere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is a 95%confidence interval for the population slope 尾1?

a.3.0867卤0.4117

b. 3.0867卤0.8518

c.3.0867卤0.8069

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e.localid="1654193042763" 3.0867卤0.8481
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