Chapter 8.1, Problem 26E

a.

To determine

To construct: A scatterplot using the provided data set.

Explanation of Solution

Given:

The data set is:

Brother	Sister
71	69
68	64
66	65
67	63
70	65
71	62
70	65
73	64
72	66
65	59
66	62

Graph:

The figure could be constructed as:

  

Interpretation:

From the above plot, it is clear that there is a weak positive correlation between the two variables.

b.

To determine

To find: The least square equation.

Answer to Problem 26E

The least square equation is $\widehat{y}=27.635+0.527x$

Explanation of Solution

From Ti-83 calculator the output is:

  

Thus, the equation of the regression line is $\widehat{y}=27.635+0.527x$

c.

To determine

To find: The height of Tonya if it is given that Damien is 70 inches.

Answer to Problem 26E

The height is 64.525 inches.

Explanation of Solution

The height of Tonya can be calculated as:

  $\begin{array}{c}\widehat{y}=27.635+0.527x\\ =27.635+0.527\left(70\right)\\ =64.525\end{array}$

Thus, the required height is 64.525 inches.

d.

To determine

To explain: Whether the prediction is highly accurate or not.

Explanation of Solution

Coefficient of determination using Ti-83 calculator can be calculated as:

  

Interpretation:

Since, the coefficient of determination is not so high. Thus, the model is not highly accurate.