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Dear Allstat .....

I have a problem with expressing a confidence/prediction interval around a
regression line (model) that would make sense easily to medical clinician
colleagues.

The situation is as follows. The dataset is N=300,000 approx and I am using
standard multiple regression techniques to contrast two models having the
same dependent variable (birthweight  at full term pregnancy) with firstly
... A: 2 co-variates (1 binary, 1 scale) and then ... B: 11 co-variates (a
mixture of binary, categoric and scale).

Particularly relevant statistics are given as follows:

A: Constant = 3553; SEE = 442: R-square = 0.180.

B: Constant = 3511; SEE = 411; R-square = 0.291

Now, clinicians understand the concept of R (correlation explaining the
'fit' of the model), R-square (coeff of determination describing the
percentage of variation in birthweight explained by the co-variates present)
and SEE (Std error of estimate = sd of model residuals as a way of
describing variation around the model).

However, they seem nervous about the fact that the increase in R-square
(about 62%) is reflected only in a corresponding decrease in SEE (approx
7%). Even if I convert R-square to R, the increase is still large (27%)
compared with the SEE decrease. When I attempt to convert these statistics
to diagrams, the results are quite uninspiring, since the population sampled
is so large and the corresponding intervals so small as a result.

Question 1: Has anyone any suggestions on how I might explain the above
statistics in a way that might make sense to my colleagues?

SPSS has a facility for calculating 'individual confidence intervals' (LICI
and UICI) which seem much wider than I personally obtain for standard
confidence/prediction intervals.

Question 2: I cannot find any information on these! Does anyone know (or can
they refer to) how these are calculated?

Thanks in advance.

Andre Francis
Perinatal Institute
Birmingham
United Kingdom

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