[EMAIL PROTECTED] wrote:
> Hi Paige,
>
> [snip]This is pretty standard stuff. For example, on page57 of Kleinbaum and
> Kuppers book Applied Regressions Analysis..., confidence bands are
> graphically displayed for a regression model. The bands get wider towards
> the ends of the regression slope, thus illustrating wider variation in the
> extremes. The width of the confidence band is a function of the standard
> error of the estimated y value at each level of the predictor variable. I
> remember as a student asking Jamie Algina why this occured but did not get
> an answer, and have not heard one since. Perhaps the band gets wider when
> the predictor (x) is normally distributed but not when x is uniformly
> distributed?
Check out Wine, R. Lowell, Statistics for Scientists and Engineers,
Prentice-Hall, Inc., Englewood Cliffs, NJ , 1964 LCCN: 64-17363
The confidence band for a linear regression estimate is a quadratic, with
(x-x_bar)^2 as a key term, and Sum of Squares of x as another. Thus, the CI
gets wider as you go away from the center of the x data - the x_bar. Also, if
you put all your data at either end of the x 'space' you minimize 1/SSx and
make the confidence band as narrow as possible. Of course, this assumes that
you believe firmly in the suitability of the linear model :)
these terms come out of the derivation for the confidence interval and involve
the usual 4 assumptions for a regression analysis.
Cheers,
Jay
--
Jay Warner
Principal Scientist
Warner Consulting, Inc.
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