25.1 Tree

To determine the amount of timber that can be extracted from a forest area, equations or tables are often used to estimate the tree's volume as a function of its diameter and/or its height. The file TREE.MTW contains information on 31 trees of a certain type. The data is from B.F. Ryan, B.L. Joiner and T.A. Ryan, Jr, Minitab Handbook, 2nd edition (© 1992 Brookes/Coles, a part of Cengage Learning, Inc. reproduced by permission. www.cengage.com./permissions). The file is organized as follows:

Column | Content |

C1 | Tree diameter at a certain distance from the ground (in cm) |

C2 | Tree height (in m) |

C3 | Volume of useable timber (in dm3) |

The aim is to find an equation to determine the timber volume of this type of tree as a function of the diameter, height, or both.

The bivariate plots (Graph > Matrix Plot > Each Y versus each X: Simple) clearly show that the best model with only one regressor is the one that explains the volume as a function of the diameter. In the following, this model is studied in detail:

Stat > Regression > Regression

The plots for the residual analysis (in the dialog box Regression, press button Graphs and choose Four in one) look as follows:

The most notable issue is that in the second graph, residuals versus fitted values (Versus ...

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