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Given in the question that the animal species produce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pinecones, a food source that sometimes has very large crops. Researchers collected data on an index of the abundance of pinecones and the average number of offspring per female over $16$years.

General least-squares equation:

The coefficients $a$ and $b$ are given in the column "Coef":

$a=1.4146$

$b=0.4399$

The least-squares regression equation then becomes:

with $x$the Cone index and $y$the average number of offspring per female.

Given in the question is a computer output from a least-squares regression on these data and a residual plot.

The residual plot shows no discernible trend, and the residuals appear to be centred around $0$, indicating that the linear model is a good fit for the data.

Given in the question is a computer output from a least-squares regression on these data and a residual plot.

According to the information,

$s=0.600309$

$r^2=57.2\%$

The value of $r^2=57.2\%$means that $57.2\%$of the variation between the variables has been explained by the linear model.

The figure of localid="1650022974861" $s=0.600309$indicates that the average forecast error is aroundlocalid="1650022978588" $0.600309$.