Question

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

Short answer

The brain weight of an animal in relation to its body weight is $\hat{y}=334.765$.

Step-by-step solution

Given Information

It is given in the question:

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

Explanation

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

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

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

$\Rightarrow \log \hat{y}=2.52474$

$\Rightarrow \hat{y}={10}^{2.52474}$

$=334.765$