91Ó°ÊÓ

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 $0.600309$.