# Re: [Rd] se.fit from predict.lm

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Fri 15 Oct 2004 - 20:38:53 EST

On Fri, 15 Oct 2004, Hiroyuki Kawakatsu wrote:

> i noticed that se.fit from predict.lm is the same whether interval="conf"
> or interval="pred". it is not clear to me from ?predict.lm whether this is
> intended or not. i suggest that se.fit should match the type of interval
> requested, if interval is specified. suggested change in lm.R line 700

It is intended. It has been that way in S for many years, and lots of code relies on it. Why would it be useful to have the standard error of a prediction interval called se.fit?

```                              ^^^

>     if(se.fit || interval != "none") se <- sqrt(ip)

> to
>     if(se.fit || interval != "none") se <- switch(interval, none = ,
```
> confidence = sqrt(ip), prediction = sqrt(ip+res.var) )
>
>
> #---sample code to illustrate issue---
>
> x <- rnorm(5);
> y <- x + rnorm(5);
> out <- lm(y~x);
>
> xf <- data.frame(x=1);
> # expected y
> ye <- predict(out, xf, se.fit=TRUE, interval="conf");
> print(ye\$fit);
> print( paste("se=", ye\$se.fit) );
> # actual y
> ya <- predict(out, xf, se.fit=TRUE, interval="pred");
> print(ya\$fit);
> print( paste("se=", ya\$se.fit) );
>
> #---end of sample code---
>
> h.
> p.s. suggestion for ?predict.lm. i don't know whether the
> distinction between interval="confidence" and interval="prediction" is
> standard terminology.

It is, just as capitalizing is standard usage and you seem not to know.

> it would be clear if the help page had something
> like
> interval="confidence" accounts only for coefficient uncertainty,
> whereas interval="prediction" accounts for both coefficient and
> innovation uncertainty.

But `innovation' is not standard terminology, and it is not the coefficients that uncertain, but their estimates.

```--
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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Received on Fri Oct 15 21:09:16 2004

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