Chapter 10, Problem 23E

(a)

To determine

To find: the model makes use of this scale.

Explanation of Solution

Given:

Diameter of log	Board Feet
8	16
12	64
16	144
20	256
24	400
28	576

Calculation:

Diameter of log	Board Feet	$\sqrt{BoardFeet}$
8	16	4
12	64	8
16	144	12
20	256	16
24	400	20
28	576	24

Graph:

  

From the above output the regression equation is

  $\sqrt{BoardFeet}=Diameter-4$

Therefore, the model is $\sqrt{BoardFeet}=Diameter-4$ . This model's R-squared is 100%, which means that the model measures 100% of the uncertainty in the square root of board feet. It is an exact model and the estimates fit exactly the values in the table according to this model.

(b)

To determine

To find: the lumber number would be determined to include a log of 10 inches in diameter.

Answer to Problem 23E

36

Explanation of Solution

Given:

Diameter = 10

Calculation:

  $\begin{array}{c}\sqrt{BoardFeet}=Diameter-4\\ =10-4\\ =6\end{array}$

  $\begin{array}{c}BoardFeet=6^2\\ =36\end{array}$

Therefore, calculated lumber that a log of 10 inches in diameter is having 36 board feet.

(c)

To determine

To find: the model suggested 36 inches in diameter for log.

Answer to Problem 23E

1024 board feet

Explanation of Solution

Given:

Diameter = 36

Formula used:

Calculation:

  $\begin{array}{c}\sqrt{BoardFeet}=Diameter-4\\ =36-4\\ =32\\ BoardFeet={32}^2\\ =1024\end{array}$

Therefore, calculated lumber that a log 36 inches in diameter is having 1024 board feet.