Chapter 3.2, Problem 20AYU

(a)

To determine

To graph: scatter diagram using graphing utility.

Answer to Problem 20AYU

The scatter plot is,

  

Scatter diagram

Explanation of Solution

Given information:

In the below table $H$ represents the independent variable and $C$ the dependent variable

Height $H$   $\left(inches\right)$	Head Circumference   $C\left(inches\right)$
$25.27$	$16.4$
$25.27$	$16.9$
$25$	$16.9$
$25.27$	$17.6$
$26.5$	$17.3$
$27$	$17.5$
$26.27$	$17.3$
$26.27$	$17.5$
$27.5$	$17.5$

Concept Used:

Scatter Plot.

Calculation:

The scatter plot by the points of the table is as follows:

  

Scatter diagram

(b)

To determine

To calculate: line of best fit by using graphing utility.

Height H (inches)	Head Circumference C (inches)
$25.27$	$16.4$
$25.27$	$16.9$
$25$	$16.9$
$25.27$	$17.6$
$26.5$	$17.3$
$27$	$17.5$
$26.27$	$17.3$
$26.27$	$17.5$
$27.5$	$17.5$

Answer to Problem 20AYU

The best fit line is $C=0.373H+7.327$

Explanation of Solution

Given information:

In the below table $H$ represents the independent variable and $C$ the dependent variable

Height H (inches)	Head Circumference C (inches)
$25.27$	$16.4$
$25.27$	$16.9$
$25$	$16.9$
$25.27$	$17.6$
$26.5$	$17.3$
$27$	$17.5$
$26.27$	$17.3$
$26.27$	$17.5$
$27.5$	$17.5$

Calculation:

The best fit line is calculated by following equations:

  $\begin{array}{l}y=0.373x+7.327\\ C=0.373H+7.327\end{array}$

Conclusion:

Hence, the best fit line is $C=0.373H+7.327$

(c)

To determine

To calculated: The height of a child whose head circumference is $17.4$ inches.

Height H (inches)	Head Circumference C (inches)
$25.27$	$16.4$
$25.27$	$16.9$
$25$	$16.9$
$25.27$	$17.6$
$26.5$	$17.3$
$27$	$17.5$
$26.27$	$17.3$
$26.27$	$17.5$
$27.5$	$17.5$

Answer to Problem 20AYU

The height of a child whose head circumference is $17.4$ inches is $27.005$ .

Explanation of Solution

Given information:

In the below table $H$ represents the independent variable and $C$ the dependent variable

Height H (inches)	Head Circumference C (inches)
$25.27$	$16.4$
$25.27$	$16.9$
$25$	$16.9$
$25.27$	$17.6$
$26.5$	$17.3$
$27$	$17.5$
$26.27$	$17.3$
$26.27$	$17.5$
$27.5$	$17.5$

Calculation:

The height is calculated by:

  $\begin{array}{l}C=0.373H+7.327\\ 17.4=0.373H+7.327\\ C=27.005\end{array}$