Statistics.....Re-Expressing Data: Get It Straight!!!?

Re-Expressing Data: Get It Straight!

32. Tree growth. A 1996 study examined the growth of grapefruit tress in Texas, determining the average trunk Diameter (in inches) for trees of varying Ages:

Age (yr)
2
4
6
8
00
12
14
16
18
20
Diameter (in inches)
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?

here is my model.
http://i36.tinypic.com/xu7tk.jpg

The scatterplot is OK, but since I do not observe a linear pattern, what can I do in order to create an appropriate 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.

I would expect the fit to be less strong. If data had been given for individual trees instead of averages, the deviation between trees’ diameter would be large. For example, trees’ diameter in individual age could be add or subtract 5; therefore, the diameter might be unstable. It could be increasing or decreasing. As a result, we could not fit a linear model from these data.

AM I RIGHT???