Need Help: 95% Confidence Interval not Equal to Estimate +/- 1.96 times of SE

[Moon Underwood]

I need some help for the standard error and 95% confidence interval. My understanding is that the 95% confidence interval should be the estimate +/- (1.96 x Standard Error). However, when I ran the following codes, the reported 95% confidence interval is quite different (see attachment regression results). Can anyone help explain why Stata gave me such results? Thank you very much.

clear
input float prod_x byte(year month)
5.2 1 1
5.4 1 2
6.3 2 1
6.5 2 2
end
 

regress prod_x i.year

Example.pdf

[Carlo Lazzaro]

Moon:
please note that, as per FAQ, attachment are discouraged on this forum.
Use CODE delimiters instead thanks.
That said, please note that the 95% CIs in OLS are calculated according to the t distribution, that takes degrees of freedom into account.

[Joro Kolev]

Elaborating on Carlo's explanation, the difference is because you have very few degrees of freedom, so the critical t-value which is used by Stata is very different from 1.96.

Here is the calculation:

. regress prod_x i.year

      Source |       SS           df       MS      Number of obs   =         4
-------------+----------------------------------   F(1, 2)         =     60.50
       Model |  1.21000031         1  1.21000031   Prob > F        =    0.0161
    Residual |  .040000019         2   .02000001   R-squared       =    0.9680
-------------+----------------------------------   Adj R-squared   =    0.9520
       Total |  1.25000033         3  .416666778   Root MSE        =    .14142

------------------------------------------------------------------------------
      prod_x |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      2.year |        1.1   .1414214     7.78   0.016      .491513    1.708487
       _cons |        5.3         .1    53.00   0.000     4.869735    5.730265
------------------------------------------------------------------------------

. dis "Lower bound of 95% CI = " _b[2.year] - invttail(2,.025)*_se[2.year]
Lower bound of 95% CI = .49151301

. dis "Uper bound of 95% CI = " _b[2.year] + invttail(2,.025)*_se[2.year]
Uper bound of 95% CI = 1.7084873

and the critical value is not 1.96, but rather

. dis invttail(2,.025)
4.3026527

[Moon Underwood]

Thank you both for the explanation.