Tree volume estimation

Developing Data Products

Coursera assignment

Johns Hopkins University

• The trees data set is bundled with R
• It allows to model the volume of wood in trees
• Given two predictors
• Lumberjacks all over the world are wondering now
• What is the right model?

head(trees)

  Girth Height Volume
1   8.3     70   10.3
2   8.6     65   10.3
3   8.8     63   10.2
4  10.5     72   16.4
5  10.7     81   18.8
6  10.8     83   19.7

• The predictors are girth (g) and height (h)
• Girth is a circumference type measure
• Volume is a cubic measure, for a cone \( V \propto A h \)
• Since \( g \propto r \), \( A \propto r^2 \), \( A \propto g ^ 2 \)
• But note that trees aren't cones,
• Trees are often considered fractals
• So a good model could easily involve fractional exponents
• Let's see a \( V \propto g^2 h \) model's results