With respect to desiginingt eh regression model, the variability in the
predicted values increases as the value being predicted from (X) differs
from its mean. The standard error of y predicted given x (from Graybill &
Iyer, 1994) is sigma-hat times the square root of [1 + 1/n +
((X-M(X))^2/SS(X))]. Thus, if you want more accurate prediction at the
extremes as well as the middle, you need to increase n and in particular
oversampe the extremes so that the sum of squares of x is larger and the
particular squared deviation becomes a smaller piece of the whole. If you
just randomly sample with few observations in the tails, then you will have
much less precision in predicting those extremes.
As far as adding new predictors, add observations to maintain the
appropriate level of power for the analysis.
Paul R. Swank, Ph.D.
Professor, Developmental Pediatrics
Medical School
UT Health Science Center at Houston
Hi All - would appreciate advice on the following:
I have an established Multiple Regression model (12 or so independent
variables). Is there a standard procedure for adding in new independent
variables at a later date (say 3 new variables)? Is there a criterion for
how much additional data to collect? Any advice here?
Designing a new Regression model (Single or Multiple - not sure yet) I'm
unsure as to nature of data I should collect (X data is panel `sizes' on
cars, trying to predict Y panel repair times from panel information). How
should I sample those X cases in population that do not occur often in
practice (smallest panel repairs, largest panel repairs), and which will
not be predicted often - BUT will nevertheless feature from time to time.
Thing is the population of variables are mostly `middle-scale' repairs, and
this is where regression model will be required most often. Should I sample
over all `sizes' irrespective of how often they feature in practice, or
instead just concentrate on those x-values that appear most often?
Any particular books/sources useful for these sorts of issues?
many thanks in advance.
Murray Doyle
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