How to construct a 95% confidence interval for a solved regression equation?

[Dylan Hambleton]

I have solved a regression equation in order to find a CEO's salary after ten years. The equation is as follows:


Salary = (Coef. of _cons) + (Coef. of ceo variable) * (10 years)

or

Salary = 772.4263 + (11.74613)*(10) = 889.8876 or $889,887.60


I would now like to construct a confidence interval which predicts the average CEO salary after ten years. I would also like to find the upper and lower bounds of this prediction. However, if I plug in the ceo variable and salary variable into the ". ci" command, the numbers do not make sense. How would I predict these bounds which properly match the solved ceo salary?


Also, how would I show these boundaries graphically on a scatter plot alongside the regression line?

Thank you.

[Carlo Lazzaro]

Dylan:
you can take advantage of some of the -predict- commands (see -regression postestimation- entry in Stata .pdf manual) for your forecast, as you can see in the following toy-example:

. use "C:\Program Files\Stata16\ado\base\a\auto.dta"
(1978 Automobile Data)

. regress 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
------------------------------------------------------------------------------

. predict fitted, xb

. predict fitted_se_forecast, stdf

. list make fitted fitted_se_forecast in 1/10

     +-------------------------------------+
     | make              fitted   fitted~t |
     |-------------------------------------|
  1. | AMC Concord     5997.385   2641.584 |
  2. | AMC Pacer       7191.857    2651.15 |
  3. | AMC Spirit      5997.385   2641.584 |
  4. | Buick Century   6475.174   2642.218 |
  5. | Buick Electra   7669.646   2662.385 |
     |-------------------------------------|
  6. | Buick LeSabre   6952.962   2647.112 |
  7. | Buick Opel      5041.808   2653.088 |
  8. | Buick Regal     6475.174   2642.218 |
  9. | Buick Riviera   7430.751   2656.243 |
 10. | Buick Skylark   6714.068   2644.134 |
     +-------------------------------------+

.

Then you can calculate the 95% CI assuming normality.
Otherwise, you can compute a bootstrapped 95% CI around the -fitted- values (see -bootstrap- entry in Stata .pdf manual).

[Carlo Lazzaro]

Dylan:
you can take advantage of some of the -predict- commands (see -regression postestimation- entry in Stata .pdf manual) for your forecast, as you can see in the following toy-example:

. use "C:\Program Files\Stata16\ado\base\a\auto.dta"
(1978 Automobile Data)

. regress 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
------------------------------------------------------------------------------

. predict fitted, xb

. predict fitted_se_forecast, stdf

. list make fitted fitted_se_forecast in 1/10

     +-------------------------------------+
     | make              fitted   fitted~t |
     |-------------------------------------|
  1. | AMC Concord     5997.385   2641.584 |
  2. | AMC Pacer       7191.857    2651.15 |
  3. | AMC Spirit      5997.385   2641.584 |
  4. | Buick Century   6475.174   2642.218 |
  5. | Buick Electra   7669.646   2662.385 |
     |-------------------------------------|
  6. | Buick LeSabre   6952.962   2647.112 |
  7. | Buick Opel      5041.808   2653.088 |
  8. | Buick Regal     6475.174   2642.218 |
  9. | Buick Riviera   7430.751   2656.243 |
 10. | Buick Skylark   6714.068   2644.134 |
     +-------------------------------------+

.

Then you can calculate the 95% CI assuming normality.
Otherwise, you can compute a bootstrapped 95% CI around the -fitted- values (see -bootstrap- entry in Stata .pdf manual).

[Dylan Hambleton]

Thanks!

[Dylan Hambleton]

So I tried the first option using the fitted value, and once I use the ci means command for the fitted value, the confidence interval is the same as the means. Why is this? What did I do wrong?

[Carlo Lazzaro]

Dylan:
as per FAQ, could you please share what you typed and what Stata gave you back with both the approaches that you followed? Thanks.