Empirical Modeling: Day 9

Last time

Next time

Announcements
- Reminder: please keep the phones out of sight and sound.
- Your group projects are (not yet) returned.
  We'll talk about those in a bit.
  I am preparing my own report, incorporating some of your work (and especially your references -- good job hunting down interesting information!).
  I want each group to submit one more thing: all the markings missing from Dave's stick for a 10 foot log, obtained using a stated equation (by Friday).
- You have a homework problem (due Wednesday), related to doing a regression -- by hand.
Last time:
- We derived the linear regression equations, using linear algebra. We didn't quite finish, so we'll go there first today.
- Again, the advantage of this approach is that it can be generalized, as we will do today.
Today:
- We finish the derivation of the linear regression equations, using linear algebra.
- We are going to discuss using linear regression and identifying the Ontario Log Rule from data.
  But first, some comments. No one got it right. That's okay! But let's learn from our mistakes.
  #1: avoid the use of first person singular in a group report. A) I've got no idea which "I" it refers to; B) it makes me wonder about the functioning of the group!
  1. I liked that Jared et al. tried the log-log transform, and got a pretty damned good fit with it. It's wrong, but it was beautiful!:)
    Let's take a look at the derived equation and "regression diagnostics" (more about regression diagnostics later).
  2. Luke et al. figured out the answer, but then did an unusual regression -- getting very close, but slightly off the mark.
    I really loved the format of your report. Everyone check that out. Let's start developing sections along these lines.
  3. Sean et al. discovered the Ontario Rule in their 12 ft. quadratic regression -- but didn't mention it!
    Also nice graphic, page 1.
  4. Kate et al. horned right in on the Ontario Rule; but then got off track, suspecting the use of two different rules.
  5. Proctor et al. also discovered the Ontario Rule, but based on the fact that the stick says "Ontario" on it! I need more!
    This group did a nice quadratic regression, but didn't indicate which length it pertained to. I think that they did 14 foot logs, based on the coefficient for the quadratic term ($x^2$). Why do I think that?
- So: before we go any further, new groups:
```
Name	GroupLabel
Adheke	A2
Adkins	E2
Browe	B2
Demler	D3
Field	C1
Flerlage	A3
Ford	C2
Kaelin	C3
Mercer	E1
Monroe	E3
Moore	D2
O'Shaughnessy	B3
Quinn	D1
Slavey	A1
Van Laningham	B1
```
  Cycle: #1s stay fixed. #2s, shift one letter "up" (or wrap); #3s, shift two letters "up"
  So C1, B2, and A3 is a new group, as is A1, E2, and D3 is a new group. And so on....
  These are the new groups for your next group project (on our assignment page), which will be due next Friday.
  Let's get into those groups, and then all run some quadratic regressions on the stick data.
  We do need to be careful however, for the eights data. It's offset from the others....
Links:
- "The IPCC stands by its equation of 450 ppm = 2 degrees C [of warming]....": For years scientists have said that if atmospheric levels of carbon dioxide reach 450 parts per million (ppm) the planet would heat up by an average of 2 degrees Celsius above pre-industrial levels. They have also said that if the world crosses that threshold, ecosystems worldwide would suffer serious damage.

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