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I thank Jacob for inspiring me to play around a little with the InsightMaker programming features.
And the answer is: order of operations.
Let's see what the problem is. Some people say "Don't force your regression through zero just because you know the true intercept has to be zero", but there are times to force your regressions through zero when you know that the true intercept has to be zero!
So why should the intercept be zero?
InsightMaker should have thrown an error with this intercept-included model if you used an intercept, and set moose to 200 to start.
Interestingly enough, you could estimate this model using either linear or non-linear regression (which give the same results in the model with intercept term, but dramatically different $R^2$ values in the non-intercept case).
As we discussed in class, we expect that the kill-rate should level off, since the wolves are satiated at some point. They just can't kill any more! They're already stuffed....
What about when the moose/wolf ratio is near 0?
Review your own city's rainfall report (and collaboration), and compare and contrast the two reports for your two previous cities. Three pages, typed. Due Monday, 3/26.
We begin the back end of the course talking about stochasticity and probabilistic models. The first examples will be Markov Chains, and we'll use one in a familiar context -- an SIR -- to get acquainted.
We'll be talking about states, and transitions between states, and we'll be using matrices to represent our transitions, vectors for our states, and those matrix operations we discussed earlier to see into the future.
Along the way I'll make use of trees, and graphs, two standard structures in discrete math. The former will give us some insight into fractals, which we'll talk about toward the end of the course. They're fun, and surprisingly useful.
I mentioned last time that I'll be using a math modeling text by Michael Olinick as our guide. Mike visited here at our invitation a few years back, to talk about sustainability.
Markov processes have only short-term memories. They're forgetful of the past. They only look at what's right in front of their noses.
That's how you can tell that you're dealing with a Markov process!
A Markov chain models a Markov process.