Empirical Modeling: Day 7

Last time

Next time

Announcements
- Roll
- Reminder: please keep the phones out of sight and sound.
- RE: Your homework assignment you handed in last time....
  I'm not sure why, but a lot of you didn't do it all -- just the third of three problems.
  So what happened here, and how can we keep it from happening again? On day five, when I reminded you of it, I had a link (same as above) to our schedule and assignment page.
  Please keep an eye on that.
  If you did not get full credit, I'm returning it to you to fix it up by Friday. Please submit it with your group report (which is due Friday).
  Now, regarding the third problem:
  - Riegel provided "the answer":$t = 2.5988 d^{1.08283}$
    (these values are given in a table).
    Your job is to use the graph, and use the line for world-class women, and use log(coordinates), to
    1. estimate the parameters of a line, and then
    2. transform it back to a power model.
    Finally, you should EVALUATE. (UPCE) How does your answer compare to Riegel's?
Last time:
- We looked at some examples of linear regressions (including fitting quadratics, via linear regression)
- In particular, we talked about fit -- and saw some examples of poor fit, due to a poor choice of model.
- Our goal is to produce a good fit, and we need a stable of functions (such as is provided in Ben Bolker's Bestiary of functions.
- We used Mathematica to perform linear regression -- our first look at Keeling's CO₂ data. Most any mathematical software will do this.
Today:
- We will derive the linear regression equations, using multivariate calculus (next time we'll do it using linear algebra!).
- I'll turn you loose to work with your groups, in preparation for Friday's report.
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.

Website maintained by Andy Long. Comments appreciated.