Stata confidence interval as _variable

Question

Is it possible to get the regression upper and lower bound as variables so that I can predict both upper and lower bound of the regression without hard coding.

I.e

reg y x
gen ypred = _b[_cons] + _b[x]*48 \\ prediction for x = 48
gen ypred_beta95u= 0.8401741 + 0.0202769*48 \\ prediction upper bound
gen ypred_beta95l= 0.550594 + 0.0097727*48 \\ prediction lower bound

I can get the coefficients of the regression without hard coding and I want to know if it is possible to do the same thing with upper and lower bound in stata.

Read help regress postestimation and look at saved results after regression using ereturn list. — Nick Cox

dimitriy dimitriy · Accepted Answer · 2015-11-23T18:55:07

Here are two ways of doing this that rely on Stata's margins, which calculates predictions of a previously fit model at fixed values of some covariates. The first is a bit more from-first-principles. The second relies on pulling out stored estimation results that margins leaves behind.

. sysuse auto, clear 
(1978 Automobile Data)

. reg price mpg 

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     20.26
       Model |   139449474         1   139449474   Prob > F        =    0.0000
    Residual |   495615923        72  6883554.48   R-squared       =    0.2196
-------------+----------------------------------   Adj R-squared   =    0.2087
       Total |   635065396        73  8699525.97   Root MSE        =    2623.7

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -238.8943   53.07669    -4.50   0.000    -344.7008   -133.0879
       _cons |   11253.06   1170.813     9.61   0.000     8919.088    13587.03
------------------------------------------------------------------------------

. margins, at(mpg=48) level(95)

Adjusted predictions                            Number of obs     =         74
Model VCE    : OLS

Expression   : Linear prediction, predict()
at           : mpg             =          48

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |  -213.8679   1449.736    -0.15   0.883    -3103.864    2676.128
------------------------------------------------------------------------------

. /* Mostly By Hand */
. gen ll1 = _b[_cons] - invttail(`e(df_r)',0.025)*_se[_cons] 

. gen ub1 = _b[_cons] + invttail(`e(df_r)',0.025)*_se[_cons] 

. /* From Stata's own stored output */ 
. matrix E = r(table)

. matrix list E

E[9,1]
             _cons
     b  -213.86793
    se   1449.7361
     t  -.14752197
pvalue   .88313237
    ll   -3103.864
    ul   2676.1282
    df          72
  crit   1.9934636
 eform           0

. gen ll2  =  E[5,1]

. gen ub2  =  E[6,1]

. list ll2 ub1 ll2 ub2 in 1/2, clean noobs

          ll2        ub1         ll2        ub2  
    -3103.864   2676.128   -3103.864   2676.128  
    -3103.864   2676.128   -3103.864   2676.128

Stata confidence interval as _variable

1 Answers