Chapter 10

Regression

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

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. A=4.0, A- = 3.7, and B+ = 3.3. Then I average your score. If you like it, take it in place of the final exam.

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.

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: •

Model again

y

  0   1

x

1   2

x

2   3

x

3

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

It can be more than first order type equation, and have different type coefficients

:

y

  1

x

1   2

x

2  

b

11

x x

2

Why we don’t do by hand

• To solve by hand is a true nightmare, as it involves solving matrix systems: • Y = XB + error • The y’s, X’s, B’s, and error are all vectors. Y is a singular vector, B is a square matrix, X is N+1 size columns, etc.

• For example, the B’s [which are very much of interest] are given in matrix notation by: • B = (X’X) -1 X’Y

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

• http://www.stat.sc.edu/~west/javaht ml/Regression.html

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,..