BACK

 

  1. 1. Why n-1?


  1. BulletHere is the shortest possible (and still honest) answer, given by Dan Teague:


Unfortunately, there is no good/easy answer to any question in AP

Statistics that contains the phrase "why divide by (n-1)". The answer

is both always beyond the scope of the course or the student's

mathematical ability and almost always unenlightening. Moreover, with

any reasonable set of data, it makes no whit of difference if we divide

by n or n-1. Even so, (n-1) is the "right thing to do".


  1. BulletNCSSM has an activity about why n-1 that is here.


  1. 2. How do you explain R2?


Here are the two examples that most helped me explain R2 to my students.  They have been posted on the list many times over the years and I have lost track of the original author!


  1. BulletHeight explains weight.  Not totally, but roughly.  Suppose R2 is 75% for a dataset between height and weight.  We know that other things affect weight, in addition to height, including genetics, diet and exercise.  So we say that 75% of a person's variation in weight can be explained by the variation in height, but that 25% of that variation is due to other factors.


  1. BulletSuppose you are buying a pizza that is $7 plus $1.50 for each topping.  Clearly Price = 7 + 1.50(# of toppings).  Clearly r and R2 are 1 and 100%.  Does this mean that the number of toppings 100% determines my cost?  No, clearly the $7 base price has a lot to do with the price!  However, my variation in price is 100% by the variation in the number of toppings I choose.


Al Coons has an activity regarding this topic that is archived at this location.

Dan Teague gives a nice explanation of the math involved for r^2 on this archived post.

R2 was discussed on the list on this date.


  1. 3. Do I have to teach log transformations?


*Yes! 

*Why? (especially when my calculator can do it for me and has all these fancy commands!  Can't I have my students use those buttons?)

*It's on the course description!  And here's why:

*The idea of transforming data to achieve linearity is a powerful and important idea.  It is this idea we are teaching.  Re-expressing data and dealing with it in it's transformed and linear state is crucial.  As is understanding how to back-transform to make an appropriate prediction.


Dave Bock discusses transformations for linearity on this archived post.