AWARD
- There are two questions in the Kim Iles Mathematical Challenge: a theoretical one and an applied one. Make sure that you answer both of them.
- To be considered for the challenge, the solution must be submitted by June 1, 2023. Please upload your solution as a pdf file.
- The award consists of a Certificate and $100.
Theoretical question
State the Basal Area Factor for Variable Plot Sampling (in Imperial units) for the following three angles: 90 degrees, 180 degrees, and 270 degrees. You can provide a full proof or briefly illustrate the geometry (10% reduction if the geometry is missing)
Practical question
A series of diameter measurements along the stem was executed on a set of Ponderosa Pines located on the east sides of the Cascades. The data, which contains the tree number (i.e., Tree), age at the time of the measurement (i.e., Age-in years), the total height of the tree (i.e., TotalHeight-in feet), the height of the measured diameter (i.e., DiamHeight-in feet), and the diameter at the specified height (i.e., Diameter-in inches), can be downloaded HERE. You are tasked to develop a taper equation with the following requirements:
· The model can have at most four (4) parameters (Note: values estimated from the data and used in the final form of the model are considered parameters).
· Achievement of a pseudo coefficient of determination of at least 95%
· Fulfillment of all modeling requirements, with tests included.
The assessment of the models will be executed using the following criteria, in descending order of importance:
1. The number of parameters used in the model
2. Fulfillment of modeling assumptions
3. The coefficient of pseudo-determination is >=0.95
4. Smallest AIC
5. Smallest bias
6. Smallest mean square error