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 Page Number: 813 Page Number: 814 kilograms) for $96$species of mammals. The following figure 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

${\mathrm{logy}}^{\wedge }=1.01+0.72{\mathrm{logx}}^{\widehat{\log y}}=1.01+0.72\log x$

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’s weight is estimated to be about $127$kilograms (kg). How big do you expect Bigfoot’s brain to be?

Short answer

The expected brain weight is $334.734$grams.

Step-by-step solution

Given Information

Given data:

Explanation

Substituting the value of $x$in the regression equation

$\log y=1.01+0.72\log \left(127\right)$

$=2.5247$

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

$y={10}^{\log y}$

$={10}^{2.5247}$

$=334.734$