Day 6 in math modeling

• Your little assignment is due Wednesday (compute a regression equation by hand for the Keeling data). It's just a good exercise to make sure that you know how to compute with the regression equations.
• Also a reminder that your mini-projects #1 are due Friday. Remember that this is a group project, and I just want one report per group. These reports will be made available to all, because we're going to next assemble all the towns into one single model for all of Togo; so I'll need an electronic copy to post.

  If your group has any questions, feel free to stop by and talk to me!

Any questions on that?

The regression equations provided us "point estimates" for $a$ and $b$ in the model, but did not give us an confidence in those values. It would be nice to know how much confidence we have in them (and, in particular, we would like to know that the slope parameter $b$ is actually significantly different from 0).

This first contact introduces us to vector and matrix notation, and a few important operations (e.g. transpose and inverse). But the details will be left to a linear algebra course!

Matrices will be important in other models we consider, so let's be glad we meet them early.

How would you adjust things to get the quadratic fit?

• "The IPCC stands by its equation of 450 ppm = 2 degrees C [of warming]...."

• An extract from Curve Fitting via the Criterion of Least Squares, by John Alexander. A bit old-fashioned, but it's got all the major ideas, and some nice examples.

  Alexander also illustrates that one cannot simply invert the regression equation $y=a+bx$ to get the regression equation $x=\frac{y-a}{b}$. So it really matters in linear regression which variable is considered "independent" and which is considered "dependent".

• My multivariate derivation.