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Unformatted text preview: tion must be
highly nonlinear in this range). (ii) Even though the R 2 is very high (.970), the residual plot shows that there is a
clear nonlinear relation which is being missed by the linear regression. Residual 60
-60 15 20 25
Diam 30 35 2 Residual (iii) When the regression is re-run using the squared diameter, d i , the R 2 improves
from .970 to .988, indicating an improvement in the (already very high) percent
of variation in lumber volumes explained. But the most dramatic improvement is
in the residual plot, which now shows essentially no nonlinearities. 30
100 300 500
Diam^2 900 1100 The most obvious explanation here is that volume equals base area times height
for a cylinder, and evergreen tree trunks are approximately cylindrical. So
volume should be linearly related to base area ( a = π d 2 ) which in t...
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- Fall '08