 hryggcx

2022-07-09

Friesen and Shine (2019) wanted to determine whether male Australian cane toads have different testes sizes in different parts of the species' range (edge of the range vs. core of the range). As part of the study, they needed to quantify how big a toad's testes are relative to the toad's body size. They decided to perform a linear regression of total testes mass (in mg) against body mass (in g) and use the residual for each toad as a measure of the toad's relative testes size. The Coefficient Estimates table for their least-squares regression procedure is shown below.
$\begin{array}{|ccccc|}\hline \text{Term}& \text{Coefficient}& \text{Standart Error}& t-value& Pr>\mid t\mid \\ \text{(intercept)}& 19.192& 43.082& 0.44547& 0.65643\\ \text{body mass}& 3.0063& 0.36387& 8.262& 1.5733{e}^{-14}\\ \hline\end{array}$
One toad in the dataset had a body mass of 128g and a total tested mass of 163 mg. Compute the residual corresponding to this toad and write a sentence interpreting the residual. potamanixv

Expert

We have given cofficient of regression and we have to find residual for given x and y.
Let equation is
y=a+bx
Where a=19.192
b=3.0063
Where
y=19.192+3.0063x
Now we have find residual for
x=128 ,y=163
Now predicted value is
y=19.192+3.0063*128=403.9984
Now residual is
Residual=actual y-predicted y
=163-403.9984