Squirrels and their food supply ($3.2$) 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.$4$Computer output from a least-squares $4$regression on these data and a residual plot are shown here

a. Is a linear model appropriate for these data? Explain.

b. Give the equation for the least-squares regression line. Define any variables you use.

c. Interpret the values of $r^2$and $s$in context.

We need to find whether the linear model is appropriate for the given data i.e.

We know that

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

We need to find out the equation for the least-squares regression line.

We know that

The general least square eq. is given as

$\hat{y}=a+bx$

And here, $a=1.4146,b=0.4399$

Therefore, the equation is

role="math" localid="1654085044915" $\hat{y}=1.4146+0.4399x$

Where $x$is cone index and $\hat{y}$is the average no. of offsprings per female.

We need to interpret the values of $r^2$and $s$.

We know that

The value of $r^2=57.2$percent indicates that the linear model can explain $57.2$percent of the variation between the variables.

The value of $s=0.600309$indicates that the average prediction error is around $0.600309$.