Linear Statistical Models: Regression

Regression Analysis in Publications


We quickly become very accustomed to reading and interpreting regression analyses from our computer output. Regression analyses as reported in journals and other publications often look very different. Here are the results of a regression a typical analysis as produced by Stata.

use http://www.philender.com/courses/data/hsbdemo, clear

regress write female read socst i.prog

      Source |       SS       df       MS              Number of obs =     200
-------------+------------------------------           F(  5,   194) =   42.68
       Model |  9364.97492     5  1872.99498           Prob > F      =  0.0000
    Residual |  8513.90008   194  43.8860829           R-squared     =  0.5238
-------------+------------------------------           Adj R-squared =  0.5115
       Total |   17878.875   199   89.843593           Root MSE      =  6.6247

------------------------------------------------------------------------------
       write |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |   4.916003   .9478479     5.19   0.000     3.046593    6.785412
        read |   .3427226    .060063     5.71   0.000     .2242624    .4611829
       socst |   .2685807   .0584637     4.59   0.000     .1532746    .3838868
             |
        prog |
          2  |   .9975073   1.233344     0.81   0.420    -1.434978    3.429992
          3  |  -1.888857   1.389299    -1.36   0.176    -4.628927    .8512127
             |
       _cons |   18.06893   3.068803     5.89   0.000     12.01643    24.12143
------------------------------------------------------------------------------
Publication tables usually have only the regression coefficient and standard errors along with some fit statistics. In Stata, the estimates table command can be used to create publication type tables. Unfortunately, the star option is not allowed with the standard errors. Below are two examples:
estimates store m1

estimates table m1, stats(N r2 r2_a) b(%6.3f) star

---------------------------
    Variable |     m1      
-------------+-------------
      female |   4.916***  
        read |   0.343***  
       socst |   0.269***  
             |
        prog |
          2  |   0.998     
          3  |  -1.889     
             |
       _cons |  18.069***  
-------------+-------------
           N |     200     
          r2 |   0.524     
        r2_a |   0.512     
---------------------------
legend: * p<0.05; ** p<0.01; *** p<0.001

estimates table m1, stats(N r2 r2_a) se b(%6.3f) se(%6.3f) 

------------------------
    Variable |   m1     
-------------+----------
      female |   4.916  
             |   0.948  
        read |   0.343  
             |   0.060  
       socst |   0.269  
             |   0.058  
             |
        prog |
          2  |   0.998  
             |   1.233  
          3  |  -1.889  
             |   1.389  
             |
       _cons |  18.069  
             |   3.069  
-------------+----------
           N |     200  
          r2 |   0.524  
        r2_a |   0.512  
------------------------
            legend: b/se
Alternatively, you can use the outreg2 command (findit outreg2) to produce an ASCII table of the results. Note: You will usually need to add spaces manually to get the columns to line up correctly.
outreg2, see 

VARIABLES	write	Standard errors in parentheses
                        *** p<0.01, ** p<0.05, * p<0.1
female     4.916***	
          (0.948)	
read       0.343***	
          (0.0601)	
socst      0.269***	
          (0.0585)	
2.prog     0.998	
          (1.233)	
3.prog    -1.889	
          (1.389)	
Constant  18.07***	
          (3.069)	
		
Observations  200	
R-squared	0.524	
Now, let's run a second regression model with interaction and display the results of both analyses in the same table.
regress write female read i.prog##c.socst

      Source |       SS       df       MS              Number of obs =     200
-------------+------------------------------           F(  7,   192) =   31.84
       Model |  9604.82727     7  1372.11818           Prob > F      =  0.0000
    Residual |  8274.04773   192  43.0939986           R-squared     =  0.5372
-------------+------------------------------           Adj R-squared =  0.5203
       Total |   17878.875   199   89.843593           Root MSE      =  6.5646

------------------------------------------------------------------------------
       write |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |   4.961672   .9408011     5.27   0.000     3.106039    6.817305
        read |   .3478027   .0599996     5.80   0.000     .2294597    .4661457
             |
        prog |
          2  |   16.75438   6.793211     2.47   0.015     3.355472    30.15328
          3  |    8.74215   6.838349     1.28   0.203    -4.745785    22.23009
             |
       socst |    .475497   .1110706     4.28   0.000     .2564217    .6945723
             |
prog#c.socst |
          2  |   -.300757   .1274851    -2.36   0.019    -.5522081   -.0493059
          3  |   -.210099   .1386112    -1.52   0.131    -.4834953    .0632973
             |
       _cons |   7.321844   5.673858     1.29   0.198    -3.869254    18.51294
------------------------------------------------------------------------------

estimates store m2

estimates table m1 m2, stats(N r2 r2_a) b(%6.3f) star

----------------------------------------
    Variable |     m1           m2      
-------------+--------------------------
      female |   4.916***     4.962***  
        read |   0.343***     0.348***  
       socst |   0.269***     0.475***  
             |
        prog |
          2  |   0.998       16.754*    
          3  |  -1.889        8.742     
             |
prog#c.socst |
          2  |               -0.301*    
          3  |               -0.210     
             |
       _cons |  18.069***     7.322     
-------------+--------------------------
           N |     200          200     
          r2 |   0.524        0.537     
        r2_a |   0.512        0.520     
----------------------------------------
legend: * p<0.05; ** p<0.01; *** p<0.001

estimates table m1 m2, stats(N r2 r2_a) se b(%6.3f) se(%6.3f)

----------------------------------
    Variable |   m1        m2     
-------------+--------------------
      female |   4.916     4.962  
             |   0.948     0.941  
        read |   0.343     0.348  
             |   0.060     0.060  
       socst |   0.269     0.475  
             |   0.058     0.111  
             |
        prog |
          2  |   0.998    16.754  
             |   1.233     6.793  
          3  |  -1.889     8.742  
             |   1.389     6.838  
             |
prog#c.socst |
          2  |            -0.301  
             |             0.127  
          3  |            -0.210  
             |             0.139  
             |
       _cons |  18.069     7.322  
             |   3.069     5.674  
-------------+--------------------
           N |     200       200  
          r2 |   0.524     0.537  
        r2_a |   0.512     0.520  
----------------------------------
                      legend: b/se

outreg2, see
	
	         (1)       (2)		
VARIABLES	write	  write   Standard errors in parentheses	
                              *** p<0.01, ** p<0.05, * p<0.1	
female      4.916***  4.962***		
           (0.948)   (0.941)		
read        0.343***  0.348***		
           (0.0601)  (0.0600)		
2.prog      0.998    16.75**		
           (1.233)   (6.793)		
3.prog     -1.889     8.742		
           (1.389)   (6.838)		
socst       0.269***  0.475***		
           (0.0585)  (0.111)		
2.prog#c.socst       -0.301**		
                     (0.127)		
3.prog#c.socst       -0.210		
                     (0.139)		
Constant    18.07***  7.322		
            (3.069)  (5.674)		
				
Observations   200	   200		
R-squared	 0.524   0.537		


Linear Statistical Models Course

Phil Ender, 5Jan98