Multiple Regression: A Visual Approach
This course uses a visual approach to explain the concepts of
multiple regression analysis. With animated 3D computer graphics,
we can see regression surfaces and study what they reveal about
data and processes generating data.
The course should be useful to people with a wide variety of
backgrounds in statistics; the only prerequisite is knowledge of the
central ideas of an introductory statistics course. Some prior
exposure to simple regression would also be helpful.
The three sessions will cover roughly the following:
- Simple regression - how to look at bivariate data; the data
ellipsoid and the regression paradox,
- Geometry of fitting lines and planes - estimation and
hypothetical testing for the gradient; the slopes of a plane;
multiple comparisons and posterior hypotheses,
- Experimental vs. statistical control: the use of multiple
regression for control, its strengths and pitfalls,
- Regression diagnostics - wild points: when they can be
harmful and how to find them; a dynamic visual
interpretation of the standard diagnostics,
- Multicollinearity - distinguishing the symptom from the
disease; understanding interaction - a better model lets the
data tell a more interesting story, and
- Issues in variable selection.