Chapter 10, Problem 30E

(a)

To determine

To explain: the fit of a linear model to these data and what problems the model has.

Explanation of Solution

Given:

Age	Diameter
2	2.1
4	3.9
6	5.2
8	6.2
10	6.9
12	7.6
14	8.3
16	9.1
18	10
20	11.4

Calculation:

Data analysis

Data > Data analysis > Regression

Step 1. Enter data in excel spreadsheet

Step 2. Click on Data > Data analysis > Regression.

Step 3. Select input Y and X range

Step 4. Click Ok

This is the obtained output

  

Graph:

Residual Plot:

  

From the given output the regression line is $diameter=-0.463\left(age\right)+1.973$ . The R-squared value is 0.98011 which represents that 98 percent of variability in the diameter is estimated for by the model. By seeing the residual plot represents that model is not fit the data well. Thus, it is not satisfying this model

(b)

To determine

To explain: expect the fit on the basis of the data given to be better, less powerful or about the same.

Explanation of Solution

If individual trees were given diameters, rather than averages, the correlation would have been weaker. There are more complex and scattered individual observations than average observations.