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# AW: st: Confidence interval for the coefficients

 From "Martin Weiss" To Subject AW: st: Confidence interval for the coefficients Date Tue, 27 Jul 2010 18:13:05 +0200

```<>

" 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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