Chapter 7.1, Problem 32E

(a)

To determine

To Explain: a linear model appropriate for these data.

Answer to Problem 32E

Linear modal is good modal for the data

Explanation of Solution

There is not having an obvious pattern in the residual plot and the residuals looks to be centred about 0; this is telling that the linear model appears to be a good model for the data

(b)

To determine

To find: the equation for the least-squares regression line.

Answer to Problem 32E

  $\widehat{y}=1.4146+0.4399x$

With x the cone index and y the average number of offspring per female.

Explanation of Solution

The least- squares equation:

  $\widehat{y}=a+bx$

The coefficients $a$ and V are given in the column coefficient.

  $\begin{array}{c}a=1.4146\\ b=0.4399\end{array}$

The least-squares regression equation then becomes:

  $\widehat{y}=1.4146+0.4399x$

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

(c)

To determine

To Explain: the value of $r^2$ and s in context

Answer to Problem 32E

57.2% of the variation between the variables has been explained by the linear model.

The average error made when making predictions is about 0.600309

Explanation of Solution

Given:

  $\begin{array}{c}s=0.600309\\ r^2=57.2\%\end{array}$

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 value of $s=0.600309$ implies that the average error made when making predictions is about $0.600309$ .