Regression

1
Chapter 10

• Regression

2
REST OF CLASS INFO

• December 13 in TWO WEEKS is the date for our
  project presentations.
• The presentations should last approximately 15
  minutes, and include visual aids.
• The paper will be approximately 10 pages, and
  that will include data/data analysis

3
Final exam and options

• To opt out of the final, take the grade average
  of the grades that that the other students will
  give you for the presentation. Since there are
  22 total students, each student will give 8A,
  8A-, 4B one of each grade, in other words to
  each other presentations. A4.0, A- 3.7, and
  B 3.3. Then I average your score. If you
  like it, take it in place of the final exam.

4
Final Exam

• I will hold the final exam Thursday, December 20,
  2001 at the same time/same place.
• It will be a cooperative, open book effort.
• I will get some very interesting manufacturing
  data.

5
Now for more stuff

• We have done enough factorials
• LINEAR REGRESSION is also a very useful topic,
  and is Chapter 10
• This is my favorite topic, it should be right
  after Chapter 2.
• Instead of hypothesis testing, or estimating a
  mean, realize that we could very well be
  estimating the coefficients of the model

6
Model again
7
Plot

• In other words, we see that our Y or dependent
  or response variable depends on a number of
  predictor/regressor variables.
• The idea find the equation of the line or
  function

8
It can be more than first order type equation,
and have different type coefficients
9
Why we dont do by hand

• To solve by hand is a true nightmare, as it
  involves solving matrix systems
• Y XB error
• The ys, Xs, Bs, and error are all vectors. Y
  is a singular vector, B is a square matrix, X is
  N1 size columns, etc.
• For example, the Bs which are very much of
  interest are given in matrix notation by
• B (XX)-1XY

10
The hard part

• Y XB e
• Where Y is a vector, B is a vector, X is a
  matrix, and e is a vector
• You need to solve for B

11

• http//www.stat.sc.edu/west/javahtml/Regression.h
  tml

12
Last Day of Class, December 13

• PAPER/Project REMINDERS.
• Paper PLUS Presentation
• Your data/problem will suggest the types of
  analysis. 3/4 methods eyeball, simple ANOVA,
  factorial,..