How old is that tree? One can determine how old atree is by counting its rings, but that requires cutting thetree down. Can we estimate the tree’s age simply fromits diameter? A forester measured 27 trees of the samespecies that had been cut down, and counted the rings todetermine the ages of the trees.a) Find the correlation between Diameter and Age. Doesthis suggest that a linear model may be appropriate?Explain.TTTDiameter (in.) Age (yr) Diameter (in.) Age (yr)1.8 4 10.3 231.8 5 14.3 252.2 8 13.2 284.4 8 9.9 296.6 8 13.2 304.4 10 15.4 307.7 10 17.6 3310.8 12 14.3 347.7 13 15.4 355.5 14 11.0 389.9 16 15.4 3810.1 18 16.5 4012.1 20 16.5 4212.8 22b) Create a scatterplot and describe the association.c) Create the linear model.d) Check the residuals. Explain why a linear model isprobably not appropriate.e) If you used this model, would it generally overestimateor underestimate the ages of very large trees? Explain.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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How old is that tree? One can determine how old a
tree is by counting its rings, but that requires cutting the
tree down. Can we estimate the tree’s age simply from
its diameter? A forester measured 27 trees of the same
species that had been cut down, and counted the rings to
determine the ages of the trees.

a) Find the correlation between Diameter and Age. Does
this suggest that a linear model may be appropriate?
Explain.

Diameter (in.) Age (yr) Diameter (in.) Age (yr)
1.8 4 10.3 23
1.8 5 14.3 25
2.2 8 13.2 28
4.4 8 9.9 29
6.6 8 13.2 30
4.4 10 15.4 30
7.7 10 17.6 33
10.8 12 14.3 34
7.7 13 15.4 35
5.5 14 11.0 38
9.9 16 15.4 38
10.1 18 16.5 40
12.1 20 16.5 42
12.8 22

b) Create a scatterplot and describe the association.
c) Create the linear model.
d) Check the residuals. Explain why a linear model is
probably not appropriate.
e) If you used this model, would it generally overestimate
or underestimate the ages of very large trees? Explain.

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