Maple Worksheet
Math 356
March 15, 2007

Problem 4.3.7 on page 158 once again talks about our friends, the ponderosa pines. The data is given in the book, and Prof. Chris has transcribed the data to the end of the Empirical Models worksheet. Your task: use the methods from Chapter 4 to determine a good model for the data, ignoring what we may remember from previous interactions with the data. That is:

  • First, comb over the data, and remove any outliers.
  • Then, find a reasonable one-term model.
  • Find the high-order polynomial that fits the data.
  • Determine the degree of a low-order polynomial that fits the data, and then find the polynomial of that degree that fits the best.
  • Find a cubic spline that fits the data.
Once you have come up with your four models, determine with your group which one is the best one. You'll have to determine what you mean by "best", and then justify why you've chosen your choice. Remember, some tools you might wish to use are:
  • Visual inspection
  • Residual plot
  • Regression and the R^2 coefficient.
We'll discuss your answer in class today or tomorrow.
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