[R] understanding predict.lm

[John Fox]

Dear Spencer,

You need the t distribution with correct df, not the standard-normal 
distribution:

 > pt(-z.confInt/2, df=13)
     1     2     3     4     5     6     7     8     9    10    11
0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025
    12    13
0.025 0.025

 > pt(-z.predInt/2, df=13)
     1     2     3     4     5     6     7     8     9    10    11
0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025
    12    13
0.025 0.025

I hope this helps,
  John
-- 
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://www.john-fox.ca/

On 2023-11-06 4:16 p.m., Spencer Graves wrote:
> Caution: External email.
> 
> 
> Hello, All:
> 
> 
>           I am unable to manually replicate predict.lm, specifically 
> comparing
> se.fit with (fit[,3]-fit[,2]): I think their ratio should be
> 2*qnorm((1-level)/2), and that's not what I'm getting.
> 
> 
>           Consider the following slight modification of the first 
> example in
> help('predict.lm'):
> 
> 
> set.seed(1)
> x <- rnorm(15)
> y <- x + rnorm(15)
> predict(lm(y ~ x))
> new <- data.frame(x = seq(-3, 3, 0.5))
> predict(lm(y ~ x), new, se.fit = TRUE)
> pred.w.plim <- predict(lm(y ~ x), new, interval = "prediction",
>                         se.fit = TRUE)
> pred.w.clim <- predict(lm(y ~ x), new, interval = "confidence",
>                         se.fit = TRUE)
> 
> (z.confInt <- with(pred.w.clim, (fit[,3]-fit[,2])/se.fit))
> pnorm(-z.confInt/2)
> 
> s.pred <- sqrt(with(pred.w.plim,
>                      se.fit^2+residual.scale^2))
> (z.predInt <- with(pred.w.plim, (fit[,3]-fit[,2])/s.pred))
> pnorm(-z.predInt/2)
> 
> 
>           ** This gives me 0.01537207. I do not understand why it's not 
> 0.025
> with level = 0.95.
> 
> 
>           Can someone help me understand this?
>           Thanks,
>           Spencer Graves
> 
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