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Tree growth A 1996 study examined the growth of grapefruit
Chapter 9, Problem 28RE(choose chapter or problem)
Problem 28RE
Tree growth A 1996 study examined the growth of grapefruit trees in Texas, determining the average trunk Diameter (in inches) for trees of varying Ages:
Age (yr) |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
Diameter (in.) |
2.1 |
3.9 |
5.2 |
6.2 |
6.9 |
7.6 |
8.3 |
9.1 |
10.0 |
11.4 |
a) Fit a linear model to these data. What concerns do you have about the model?
b) If data had been given for individual trees instead of averages, would you expect the fit to be stronger, less strong, or about the same? Explain.
Questions & Answers
QUESTION:
Problem 28RE
Tree growth A 1996 study examined the growth of grapefruit trees in Texas, determining the average trunk Diameter (in inches) for trees of varying Ages:
Age (yr) |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
Diameter (in.) |
2.1 |
3.9 |
5.2 |
6.2 |
6.9 |
7.6 |
8.3 |
9.1 |
10.0 |
11.4 |
a) Fit a linear model to these data. What concerns do you have about the model?
b) If data had been given for individual trees instead of averages, would you expect the fit to be stronger, less strong, or about the same? Explain.
ANSWER:
Step 1 of 4
a)
First we will try to create the linear model for the data.
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 |