Chapter 4.4, Problem 19E

a.

To determine

To make: a scatter plot using the collected data and then draws a line of fit for the data.

Answer to Problem 19E

  $y=0.82x+\mathrm{34.08.}$

Explanation of Solution

Given information: The arm span and height of five people are given in below table.

Person #	Arm Span( cm )	Height( cm )
1	156	162
2	162	170
3	173	185
4	188	187
5	194	193

Formula Used:

The point-slope form of the line is:

  $\begin{array}{l}y-y_1=m(x=x_1)\\ \text{where}m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

Calculation:

The scatter plot using the table data is given below.

  

Write an equation of the line using 2 points.

  $\begin{array}{l}(x_1,y_1)\to (156,162)\\ (x_2,y_2)\to (194,193)\end{array}$

  $\begin{array}{c}y-y_1=m(x=x_1)\\ \text{where}m=\frac{y_2-y_1}{x_2-x_1}=\frac{193-162}{194-156}\approx 0.82\\ \text{Substitute}\text{given:}\\ y-162=0.82(x-156)\\ y-162=0.82x-127.92\\ y=0.82x+\mathrm{34.08.}\end{array}$

b.

To determine

To interpret: the slope and y - intercept of the line of fit.

Answer to Problem 19E

  $y=0.82x+\mathrm{34.08.}$

The slope represents the increase of 0.82 cm in height for an increase of 1 cm in arm span.

The y −intercept represents a height of 34.08 cm for an arm span of 0 which makes no sense or is impossible.

Explanation of Solution

Given information:

Calculation:

  $y=0.82x+\mathrm{34.08.}$

The slope represents the increase of 0.82 cm in height for an increase of 1 cm in arm span.

The y −intercept represents a height of 34.08 cm for an arm span of 0 which makes no sense or is impossible.