[R] confidence interval in "predict.lm"
Peter Dalgaard BSA
p.dalgaard at biostat.ku.dk
Fri Nov 15 19:18:56 CET 2002
"Fred Mellender" <fredm at frontiernet.net> writes:
> The book gives the confidence interval as 26.5 <= y <= 39.5. The book
> defines the confidence interval calculation thus:
>
> yp - E <= y <= yp + E
>
> Where
> E = tc*sC *sqrt(1 + 1/n + (x-xBar)^2/SSx)
> yp is the predicted value from the regression line
> tc is the value from Student's t distribution for a confidence
> level, c, using n-2 degrees of freedom,
> sC is the standard error of estimate
> SSx is Sum(x^2)-[Sum(x)]^2/n
> n is the number of data pairs.
>
> So that even though the model, predicted value, standard error all agree, R
> gives a much smaller confidence
> interval than the book does.
>
> Thanks for any advice/help.
The book is giving you a prediction interval, aka a tolerance
interval. Some people use the term "confidence interval" a bit too
sloppily. predict() will give you the other kind of interval if you
ask it to. Vice versa,
E = tc*sC *sqrt(1/n + (x-xBar)^2/SSx)
would give you the confidence interval for the predicted mean, I think.
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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