[R] Beginner's Question on Linear Regression Models

John Fox
Sat, 21 Jun 2003 12:08:35 -0000

Dear James,

A very nice way of understanding these matters intuitively is to express
them geometrically using data and confidence ellipses (for two predictors
and their coefficients) and ellipsoids (more generally). The same ideas
apply to linear hypotheses, such as for the difference between two
coefficients. A good elementary treatment may be founds in Georges Monette,
"Geometry of multiple regression and 3-D graphics," in Fox and Long
(eds.),
Modern Methods of Data Analysis, Sage, 1990. Some regression texts also
develop the geometry of regression and linear models.

I hope that this helps,
  John

At 04:04 AM 6/21/2003 -0700, J Ireland wrote:
>Hi Folks,
>
>Could anyone point me to a good reference on linear regression
>models?   Specifically, I am trying to gain an intuitive feel for how the
>standard error values are calculated for the parameter estimates.  My
>understanding is that these are computed using the variance-covariance
>matrix computed from the input data matrix.  Although I think I understand
>the math, I still don't have a good gut feel for why one parameter is
>attributed with a larger standard error than the next parameter.
>
>Also, I am interested in knowing how to test that two parameters are
>significantly different from one another.
>
>Thanks in advance for your help.
>-James

-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox