SOLN_3b

970 to 988 indicating an improvement in the already

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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 20 -20 -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 10 -10 -30 -50 100 300 500 700 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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