### Regression Models: Building Simple Models from Sample Data

#### See Jain, Chapters 14 and 15

#### What should I know?

- Response variable vs. predictor variables

- Motivation for regression models:
- Investigate dependence of one variable on others.
- Extrapolate.

- Types of regression models:
- Simplest case: linear with one predictor
- Multiple linear
- Nonlinear

- How to compute a regression model --- use software tools!
For example, Excel, SAS,
JMP,
ExpertFit.

- Meaning of ``least squares fit.'' If the model is
,
where the function is defined by
*k* parameters
,
then the least squares fit corresponds to choosing the parameters
to minimize

- Allocation of variation. The
*coefficient of determination* is
defined as

where

- Computing confidence intervals for regression parameters (see 14.5):
- From the standard deviation of the sample errors,
we can compute ...
- standard deviations for each regression parameter, from which we
can compute ...
- confidence intervals for the ``true'' parameters,
(typically using a t-distribution).

- Computing confidence intervals for predictions (future values),
see 14.6.

- Importance of visual tests for goodness of fit. See 14.7.

- What about non-numerical predictor variables? See 15.2.

- A note on polynomial models.
- If the model is
*y = a x^b*, then do simple linear
regression on *log(y) = log(a) + b log(x)*.
- If the model is
*y = a + bx^m* (for assumed *m*),
then do simple linear regression on
*y = a + b (x^m)*.

CS 5014,
C. J. Ribbens,
10/03/2001