Statistics...HELP!!!?

alvinchou2003

2008-08-19 6:48 pm

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 you do not observe a linear pattern, what can you do in order to create an appropriate model?

There's a pretty obvious curve to the data. Chapter 10 is about re-expressing data. What re-expression would work here?

PLS HELP!!!

回答 (1)

[匿名]

2008-08-19 8:59 pm

✔ 最佳答案

You have x and y reversed, with age as the y-axis and diameter on x-axis

It appears growth in the early years is faster,
but after that it approximates linear growth using
Diameter = 4.6 + 2/5 (age - 4)
We get this data:
Years Diameter (actual)
2 3.8 (1.9) [ not so good on this one ]
4 4.6 (3.9)
6 5.4 (5.2)
8 6.2 (6.2)
10 7 (6.9)
12 7.8 (7.6)
14 8.6 (8.3)
16 9.4 (9.1)
18 10.2 (10.0)
20 11 (11.4)

Here is your picture with a line added: http://i37.tinypic.com/28mixyw.jpg
Below 4 years growth is faster, so we have start at age 4.

Tweaking the numbers a bit might make it closer on
more points, but anyway, you get the idea.
=

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