Analysis of Tree Data
This is a comparison of how much lumber a tree will produce given its age in years. Given the following data:
We can make predictions based on the behavior of this data. Using an Excel spreadsheet, we can model this data using some sort of exponential growth. Exponential growth curves are “nice” for approximation primarily because they are smooth and the end-behavior is very clear (it’s going up!). But, this graph isn’t truly exponential because it is not quite as steep and the age of a tree vs. its age is hardly exponential (as compared to situations such as population growth). So, we should consider other smooth curves such as a polynomial. Even-powered polynomials make the best choices because they also have an end behavior of increasing to infinity. Odd-powered polynomials are not as reliable since one side is always decreasing. We are most familiar with polynomials of degree 2, so a quadratic equation would make an appropriate approximation.
As you can see, a quadratic regression line is very good. However, we can get a better line:
We are missing some ages of tree data. Using this function model, we can predict how much lumber a sixty-year old tree will produce. In order to make this calculation, I will simply substitute “60” in for x in the equation model.
So, a sixty-year old tree will produce approximately 1600 board feet.
We can make similar calculations for 140 year-old and 180 year-old trees:
Thus, a 140 year-old tree will produce approximately 13,400 board feet and a 180 year-old tree will produce approximately 25,000 board feet. Based on this data, we can conclude the older the tree, the more board feet it will produce.