Re: AW: st: Confidence interval for the coefficients

[Thomas Speidel <thomas@tmbx.com>]

Thanks Martin and Michael.

Quoting Martin Weiss <martin.weiss1@gmx.de> Tue 27 Jul 10:13:05 2010:

> <>
>
>
> " Your code is perfect, except in one respect. The confidence interval is
> based on a -t-
> distribution and not a -z- distribution."
>
>
>
> But even if we accepted the -normal- as an approximation to the
> t-distribution, Thomas could improve on his ballpark "1.96" via
>
> *************
> di invnormal(.975)
> *************
>
>
>
> HTH
> Martin
>
>
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Michael N.
> Mitchell
> Gesendet: Dienstag, 27. Juli 2010 18:09
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: Confidence interval for the coefficients
>
> Dear Thomas
>
>    Your code is perfect, except in one respect. The confidence interval is
> based on a -t-
> distribution and not a -z- distribution. So, the -t- value in this case
> would be
>
> . di invttail(72,0.025)
> 1.9934636
>
>    Instead of 1.96. Substituting that into your code gives the desired
> results...
>
> . sysuse auto, clear
> (1978 Automobile Data)
>
> . reg mpg weight
>
>        Source |       SS       df       MS              Number of obs =
> 74
> -------------+------------------------------           F(  1,    72) =
> 134.62
>         Model |   1591.9902     1   1591.9902           Prob > F      =
> 0.0000
>      Residual |  851.469256    72  11.8259619           R-squared     =
> 0.6515
> -------------+------------------------------           Adj R-squared =
> 0.6467
>         Total |  2443.45946    73  33.4720474           Root MSE      =
> 3.4389
>
> ----------------------------------------------------------------------------
> --
>           mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+--------------------------------------------------------------
> --
>        weight |  -.0060087   .0005179   -11.60   0.000    -.0070411
> -.0049763
>         _cons |   39.44028   1.614003    24.44   0.000     36.22283
> 42.65774
> ----------------------------------------------------------------------------
> --
>
> .
> . di _b[weight] - invttail(72,0.025) * _se[weight]
> -.00704106
>
> . di _b[weight] + invttail(72,0.025) * _se[weight]
> -.00497632
>
> Best regards,
>
> Michael N. Mitchell
> Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
> A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
> Stata tidbit of the week         - http://www.MichaelNormanMitchell.com
>
>
>
> On 2010-07-27 8.54 AM, Thomas Speidel wrote:
> > I am sure this has been asked before, but my search did not reveal any
> > hits in the archive. Why is the following happening:
> >
> > . sysuse auto, clear
> > . reg mpg weight
> >
> > Source | SS df MS Number of obs = 74
> > -------------+------------------------------ F( 1, 72) = 134.62
> > Model | 1591.9902 1 1591.9902 Prob > F = 0.0000
> > Residual | 851.469256 72 11.8259619 R-squared = 0.6515
> > -------------+------------------------------ Adj R-squared = 0.6467
> > Total | 2443.45946 73 33.4720474 Root MSE = 3.4389
> ----------------------------------------------------------------------------
> --
> > mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
> -------------+--------------------------------------------------------------
> --
> > weight | -.0060087 .0005179 -11.60 0.000 -.0070411 -.0049763
> > _cons | 39.44028 1.614003 24.44 0.000 36.22283 42.65774
> ----------------------------------------------------------------------------
> --
> > . di _b[weight] - 1.96 * _se[weight]
> > -.00702373
> >
> > . di _b[weight] + 1.96 * _se[weight]
> > -.00499365
> >
> > Why -.00702373 != -.0070411 and -.00499365 != -.0049763 ? Rounding off
> > error/computer precision? --
> >
> > Thomas Speidel
> >
> >
> > *
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> *
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>
>
> *
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--
Thomas Speidel


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