Dennis --
Don't know as I'd care to try either of the two explanations
I've seen so far on students who weren't pretty well up on multiple
regression already; and some of _them_ I'd expect to have trouble with
the explanation involving partial correlations.
Haven't had time to look at your ancova handout -- I keep
forgetting to open it when I'm at Plymouth and could do so -- but from
the information you supply, I'd judge that the means of the covariate in
the two groups are different, and in particular that the group with the
smaller mean on the covariate lies on the higher regression line.
Visualize the "adjustment" as what would happen if you plot
dependent variable vs. covariate, labelled as to group (LPLOT in Minitab
would do this nicely); then locate the group means AND the grand mean
on the covariate; then for each group slide the group mean (and all its
attendant data points) to the right or left along that group's regression
line until the group mean coincides with the grand mean. For your data,
doing this will increase the total SS for the dependent variable (by the
518 or so that Rich Ulrich pointed out), because the group on the higher
regression line will be moved so as to make it even higher, and the group
on the lower line will become even lower.
This should be easy to illustrate on an overhead projector with
three transparencies: one displaying the two regression lines, the two
group centers of gravity [the point (Ybar,Xbar) for each group, which
will lie on the regression lines], and the grand mean of X (as a vertical
line long enough to intersect both regression lines; a second displaying
the (Y,X) data of group 1, with the center of gravity clearly marked;
and a third displaying the (Y,X) data of group 2, similarly.
-- Don.
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Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
