91Ó°ÊÓ

Brawn versus brain How is the weight of an animal's brain related to the weight of its body?

Researchers collected data on the brain weight (in grams) and body weight (in kilograms) for $96$species of mammals. The figure below is a scatterplot of the logarithm of brain weight against the logarithm of body weight for all $96$species. The least-squares regression line for the transformed data is

$\widehat{\log y}=1.01+0.72\log x$

Based on footprints and some other sketchy evidence, some people think that a large apelike animal, called Sasquatch or Bigfoot, lives in the Pacific Northwest. His weight is estimated to be about $280$pounds, or $127$kilograms. How big is Bigfoot’s brain? Show your method clearly

Step by step solution

01

Given Information

It is given in the question:

$\widehat{\log y}=1.01+0.72\log x$

02

Explanation

Bigfoot's weight is estimated to be $280$pounds or $127$ kilograms. Thus, evaluating the regression line it gives,

$\widehat{\log y}=1.01+0.72\log x$

$⇒\log \hat{y}=1.01+0.72\log \left(127\right)$

$⇒\log \hat{y}=2.52474$

$⇒\hat{y}={10}^{2.52474}$

$=334.765$

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!