Stat Computing > Stata > Web Books > Reg

Annotated Stata Output
for Listcoef Command

This page shows an example of the listcoef command with footnotes explaining the output using the elemapi2 data file. 

We first use the elemapi2 data file and then first perform a regression analysis and include the beta option. 

use http://www.ats.ucla.edu/stat/stata/webbooks/reg/elemapi2 
regress api00 ell meals yr_rnd mobility acs_k3 acs_46 full emer enroll, beta

          Source |       SS       df       MS              Number of obs =     395
    -------------+------------------------------           F(  9,   385) =  232.41
           Model |  6740702.01     9   748966.89           Prob > F      =  0.0000
        Residual |  1240707.78   385  3222.61761           R-squared     =  0.8446
    -------------+------------------------------           Adj R-squared =  0.8409
           Total |  7981409.79   394  20257.3852           Root MSE      =  56.768

    ------------------------------------------------------------------------------
           api00 |      Coef.   Std. Err.      t    P>|t|                     Beta
    -------------+----------------------------------------------------------------
             ell |  -.8600707   .2106317    -4.08   0.000                -.1495771
           meals |  -2.948216   .1703452   -17.31   0.000                -.6607003
          yr_rnd |  -19.88875   9.258442    -2.15   0.032                -.0591404
        mobility |  -1.301352   .4362053    -2.98   0.003                -.0686382
          acs_k3 |     1.3187   2.252683     0.59   0.559                 .0127287
          acs_46 |   2.032456   .7983213     2.55   0.011                 .0549752
            full |    .609715   .4758205     1.28   0.201                 .0637969
            emer |  -.7066192   .6054086    -1.17   0.244                -.0580132
          enroll |   -.012164   .0167921    -0.72   0.469                -.0193554
           _cons |   778.8305   61.68663    12.63   0.000                        .
    ------------------------------------------------------------------------------

The listcoef command can then be used after the regress command to show several types of standardized regression coefficients. 

listcoef

    regress (N=395a): Unstandardized and Standardized Estimates 

     Observed SD: 142.32844b
     SD of Error: 56.768104c

    ---------------------------------------------------------------------------
       api00d|      be        tf    P>|t|f   bStdXg    bStdYh   bStdXYi    SDofXj
    ---------+-----------------------------------------------------------------
         ell |  -0.86007   -4.083   0.000 -21.2891  -0.0060  -0.1496    24.7527
       meals |  -2.94822  -17.307   0.000 -94.0364  -0.0207  -0.6607    31.8960
      yr_rnd | -19.88875   -2.148   0.032  -8.4174  -0.1397  -0.0591     0.4232
    mobility |  -1.30135   -2.983   0.003  -9.7692  -0.0091  -0.0686     7.5069
      acs_k3 |   1.31870    0.585   0.559   1.8117   0.0093   0.0127     1.3738
      acs_46 |   2.03246    2.546   0.011   7.8245   0.0143   0.0550     3.8498
        full |   0.60972    1.281   0.201   9.0801   0.0043   0.0638    14.8924
        emer |  -0.70662   -1.167   0.244  -8.2569  -0.0050  -0.0580    11.6851
      enroll |  -0.01216   -0.724   0.469  -2.7548  -0.0001  -0.0194   226.4732
    ---------------------------------------------------------------------------

Footnotes

a. This is the number of observations that were used in the regression and hence, in the calculation of the coefficients given in the listcoef output.

b. This is the observed standard deviation; in other words, the standard deviation of the y-variable (also known as the dependent variable), in this case, api00.

c. This is the standard deviation of the error (in other words, the standard deviation of the error term). You will notice that it is the same as the Root MSE listed in the regression output. This term is also known as the standard error of prediction.

d. This is the dependent variable.  Listed below it are all of the independent variables in the model.

e. These are the unstandardized regression coefficients.  They are the same coefficients that are listed in the regression output in the column labeled coef.

f. These are the same t-tests and p-values that are listed in the regression output.  The columns in both outputs are labeled the same.  These columns provide the t value and 2 tailed p value used in testing the null hypothesis that the coefficient/parameter is 0.   If you use a 2 tailed test, then you would compare each p value to your preselected value of alpha.  Coefficients having p values less than alpha are significant.  For example, if you chose alpha to be 0.05, coefficients having a p value of 0.05 or less would be statistically significant (i.e. you can reject the null hypothesis and say that the coefficient is significantly different from 0).   If you use a 1 tailed test (i.e. you predict that the parameter will go in a particular direction), then you can divide the p value by 2 before comparing it to your preselected alpha level.  With a 2 tailed test and alpha of 0.05, you can reject the null hypothesis that the coefficient for ell is equal to 0.  The coefficient of -.86 is significantly different from 0.   Using a 2 tailed test and alpha of 0.01, the p value of 0.000 is smaller than 0.01 and the coefficient for ell would still be significant at the 0.01 level. Had you predicted that this coefficient would be positive (i.e. a one tail test), you would be able to divide the p value by 2 before comparing it to alpha.  This would yield a one tailed p value of 0.000, which is less than 0.01 and then you could conclude that this coefficient is greater than 0 with a one tailed alpha of 0.01.
   The coefficient for meals is significantly different from 0 using alpha of 0.05 because its p value of 0.000 is smaller than 0.05.
   The coefficient for yr_rnd (-19.89) is significantly different from 0 because its p value is definitely smaller than 0.05 and even 0.01.
   The coefficient for mobility is significantly different from 0 using alpha of 0.05 because its p value of 0.003 is smaller than 0.05.
   The coefficient for acs_k3 is not significantly different from 0 using alpha of 0.05 because its p value of .559 is greater than 0.05.
   The coefficient for acs_46 is significantly different from 0 using alpha of 0.05 because its p value of 0.011 is smaller than 0.05.
  

g. These are the regression coefficients with the x-variables (the independent variables) in standard deviations and the y-variable (the dependent variable) in its original units.

h. These are the regression coefficients with the x-variables (the independent variables) in original units and the y-variable (the dependent variable) in standard deviations.

i. These are the regression coefficients with both the x-variable (the independent variable) and the y-variable (the dependent variable) in standard deviations. You will notice that these are the same values given in the Beta column of the regression output.

j. This is the standard deviation of the x-variables (the dependent variables).