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# Re: st: Confidence interval for the coefficients

 From "Michael N. Mitchell" To statalist@hsphsun2.harvard.edu Subject Re: st: Confidence interval for the coefficients Date Tue, 27 Jul 2010 09:08:41 -0700

```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
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
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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```