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Industrial Statistics with Minitab by Xavier Tort-Martorell Llabres, Lluis Marco Almagro, Pere Grima Cintas

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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.
nc25uf001.eps

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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