Chapter 1.2, Problem 22E

a.

To determine

To make: a scatter plot of given data.

Answer to Problem 22E

The scatter plot of the data is show $55$ n below.

Explanation of Solution

Given:

Biologist have observed that chirping rate of crickets rate appears to be related to temperature. The given table shows chirping rates for various temperatures:

Temperature	Chirping rate(chirps per minutes)
$50$	$20$
	$46$
$60$	$79$
$65$	$91$
$70$	$113$
$75$	$140$
$80$	$173$
$85$	$198$
$90$	$211$

Calculation:

The scatter plot of the data is shown below:

  

b.

To determine

To find: the graph and regression line.

Answer to Problem 22E

  $y=-220.967+4.85667x$

Explanation of Solution

Biologist have observed that chirping rate of crickets rate appears to be related to temperature. The given table shows chirping rates for various temperatures:

Temperature	Chirping rate(chirps per minutes)
$50$	$20$
$55$	$46$
$60$	$79$
$65$	$91$
$70$	$113$
$75$	$140$
$80$	$173$
$85$	$198$
$90$	$211$

Calculation:

According to the table, to make a linear regression line and obtained the equation:

  $y=-220.967+4.85667x$

Now, graph of the regression line is shown below

  

Hence, a linear regression line model is $y=-220.967+4.85667x$ .

c.

To determine

To estimate: the chirping rate by using a linear model in part (b).

Answer to Problem 22E

  $y=264.7$

Explanation of Solution

From part (b) $y=-220.967+4.85667x$

Chirping rate is ${100}^{\circ }F$

Calculation:

According to the table, to make a linear regression line and obtained the equation:

  $y=-220.967+4.85667x$

Now, plug the value of $x=100$ , so

  $\begin{array}{l}y=-220.967+4.85667\left(100\right)\\ y=264.7\end{array}$

Hence, the chirping rate of the linear model is $y=264.7$ .