Chapter 12, Problem 12PT

(a)

To determine

To Explain: the reason that a linear model might not be suitable in this case

Answer to Problem 12PT

Curvature is residual plot

Explanation of Solution

Given:

  

  

On the basis of given information, A linear model is not ideal, since the residual plot has curvature.

(b)

To determine

To Explain: the using all models to estimate the volume of available pine lumber 30 inches in diameter from a ponderosa pine.

Answer to Problem 12PT

(1) $\widehat{y}=117.0899$

(2) $\widehat{y}=102.967$

Explanation of Solution

Given:

  

  

Calculation:

(1)

regression line of least square

  $\widehat{y}=a+bx$

The coefficients a and b are

  $\begin{array}{l}a=2.078\\ b=0.0042597\end{array}$

Then the regression line of least square is

  $\widehat{y}=2.078+0.0042597x^3$

With x=DBH and y the yield.

Putting the X by 30:

  $\widehat{y}=2.078+0.0042597{\left(30\right)}^3=117.0899$

(2)

Regression line is

  $\widehat{y}=a+bx$

The coefficients a and b are

  $\begin{array}{l}a=1.2319\\ b=0.113417\end{array}$

Then the regression line of least square is

  $\widehat{y}=a+bx$

The coefficients a and b are

  $\begin{array}{l}a=1.2319\\ b=0.113417\end{array}$

Then the regression line of least-squares becomes:

  $\text{l<mover accent="true"> n <mo>^</mo></mover> }y=1.2319+0.113417x$

With x=DBH and y the yield.

Putting x by 30:

  $\text{l<mover accent="true"> n <mo>^</mo></mover> }y=1.2319+0.113417\left(30\right)=4.63441$

(c)

To determine

To find: the prediction that is looks more reliable in part (b).

Answer to Problem 12PT

Option 1: $\widehat{y}=117.0899$

Explanation of Solution

Given:

From the part (b)

Option 1: $\widehat{y}=117.0899$

Option 2: $\widehat{y}=102.967$

Option 1 offers a more accurate estimation, since its residual plot has no apparent trend, whereas Option 2's residual plot has an apparent curvature.