Chapter 4.4, Problem 19E

a.

To determine

To graph:Data of height and arm spans of five people, draw a line of fit too.

Answer to Problem 19E

Required graph is plotted.

Line of fit is given by the equation $y=\frac{8}{7}x-\frac{118}{7}$ .

Explanation of Solution

Given Information:Data of heights and arm spans is to be used.

Graph &Calculation:

  $\begin{array}{ll}Arm\_Span\hfill & Height\hfill \\ 160\hfill & 166\hfill \\ 165\hfill & 173\hfill \\ 170\hfill & 179\hfill \\ 176\hfill & 184\hfill \\ 181\hfill & 190\hfill \end{array}$

Let us make a scatter plot of the given data.

  

Since the scatter plot shows a positive correlation, a line can be fitted to the data.

Using point-slope formula to write equation utilizing two points $(160,166)$ and $(181,190)$ ,

  $y-y_1=m(x-x_1)$

Where, $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{190-166}{181-160}\\ m=\frac{24}{21}\\ m=\frac{8}{7}\end{array}$

Substituting values in point-slope formula,

  $y-166=\frac{8}{7}(x-160)$

  $y=\frac{8}{7}x-\frac{1280}{7}+166$ (Arranging and applying distributive property)

  $y=\frac{8}{7}x-(\frac{1280-1162}{7})$ (Taking LCM)

  $y=\frac{8}{7}x-\frac{118}{7}$

Thus, the equation is $y=\frac{8}{7}x-\frac{118}{7}$ .

b.

To determine

To interpret:The slope and $y-\mathrm{int}ercept$ of the line of fit.

Answer to Problem 19E

The slope of the graph is positive a rate of $\frac{8}{7}$ .

The $y-\mathrm{int}ercept$ would represent an arm span of $0$ , which is impossible. $\therefore$ It is not even considered.

Explanation of Solution

Given Information:Data and equation from the previous part.

Interpretation:

The slope of the graph shows the rate of change of arm span (with respect to height) which is increasing at a rate of $\frac{8}{7}$ .

The $y-\mathrm{int}ercept$ would represent an arm span of $0$ , which is impossible. $\therefore$ It is not even considered.