Chapter 4.4, Problem 10PPS

(a)

To determine

The scatter-plot for the height in inches comparing to the weight in pounds.

Explanation of Solution

Given: The given data for the height in inches and weight in pounds is shown as,

Height (inches)	Weight (pounds)
62	115
63	124
65	120
67	134
67	140
68	138
68	144
68	152
69	147
72	155
73	168
73	166

Graph: The graph for the scatter-plot between the height in inches and weight in pounds is shown as,

  

Conclusion: As the height in inches increases, the weight in pounds also increases. Therefore, there is a positive correlation between the height in inches and the weight in pounds.

(b)

To determine

The graph of line of fit for the given data.

Explanation of Solution

Given: The given data for the height in inches and weight in pounds is shown as,

Height (inches)	Weight (pounds)
62	115
63	124
65	120
67	134
67	140
68	138
68	144
68	152
69	147
72	155
73	168
73	166

Graph: The graph for the line of fit using the scatter plot between the height in inches and weight in pounds is shown as,

  

(c)

To determine

The equation of line of fit in slope-intercept form.

Answer to Problem 10PPS

The equation for the line of fit is $y=\frac{29}{6}x-184.66$ .

Explanation of Solution

Given: The given data for the height in inches and weight in pounds is shown as,

Height (inches)	Weight (pounds)
62	115
63	124
65	120
67	134
67	140
68	138
68	144
68	152
69	147
72	155
73	168
73	166

Calculation: The slope $\left(m\right)$ using the points $\left(62,115\right)\text{ and }\left(68,144\right)$ for the line of fit can be calculated as,

  $\begin{array}{c}\text{Slope}\left(m\right)=\frac{144-115}{68-62}\\ =\frac{29}{6}\\ =\frac{29}{6}\mathrm{......}\left(\text{Approx}\text{.}\right)\end{array}$

Now, the line of fit having slope $\left(m=\frac{29}{6}\right)$ passes through the point $\left(62,115\right)$ . Therefore, equation of line is written using point-slope form as,

  $\begin{array}{c}y-115=\frac{29}{6}\left(x-62\right)\mathrm{......}\left(\begin{array}{l}\text{Here }m=\frac{29}{6}\text{ and}\\ \left(x_1,y_1\right)\to \left(62,115\right)\end{array}\right)\\ y-115=\frac{29}{6}x-299.66\\ y=\frac{29}{6}x-\mathrm{184.66......}\left(1\right)\end{array}$

(d)

To determine

The normal weight for a man who is 84 inches tall.

Answer to Problem 10PPS

The weight for the man will be 221.66lb (approx.).

Explanation of Solution

Given: The given data for the height in inches and weight in pounds is shown as,

Height (inches)	Weight (pounds)
62	115
63	124
65	120
67	134
67	140
68	138
68	144
68	152
69	147
72	155
73	168
73	166

Calculation: The weight for a man who is 84 inches tall can be calculated by plugging $\left(x=84\right)$ in (1). Therefore, from (1),

  $\begin{array}{c}y=\frac{29}{6}\left(84\right)-\mathrm{184.66......}\left(\text{For }x=84\right)\\ =406-299.66\\ =221.34\text{lb}\end{array}$

(e)

To determine

If the weight of the man is 188 pounds then use the equation of line of fit to find the estimated height of man.

Answer to Problem 10PPS

The height of the man will be 77.10 inches.

Explanation of Solution

Given: The given data for the height in inches and weight in pounds is shown as,

Height (inches)	Weight (pounds)
62	115
63	124
65	120
67	134
67	140
68	138
68	144
68	152
69	147
72	155
73	168
73	166

Calculation: The height for a man whose weight is 188 pounds can be calculated by plugging $\left(y=188\right)$ in (1). Therefore, from (1),

  $\begin{array}{c}\left(188\right)=\frac{29}{6}x-\mathrm{184.66......}\left(\text{For }y=188\right)\\ \text{or, }\frac{29}{6}x=372.66\\ =77.10\text{inches}\end{array}$