I need help interpreting my regression

[Nora Ross]

I don't understand how to interpret the coefficients for the dummy variables dse, dsm, de, etc. These variables represent different counties, and my dependent variable is the percentage of Catholics in a given county. For the variable dse, for example, does the coefficient mean that people in this county are 4.94 percentage points more likely to be Catholic?

[Nick Cox]

Yes, Why not work with a simple example for which you know the answer? Here is a simple case: the mean for one group is 3 and for another group is 8 and the coefficient is 5.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(catholic group)
 1 0
 2 0
 3 0
 4 0
 5 0
 6 1
 7 1
 8 1
 9 1
10 1
end


. tobit catholic i.group, ll(0) ul(100)

Refining starting values:

Grid node 0:   log likelihood = -17.655121

Fitting full model:

Iteration 0:   log likelihood = -17.655121  
Iteration 1:   log likelihood = -17.655121  

Tobit regression                                Number of obs     =         10
                                                   Uncensored     =         10
Limits: lower = 0                                  Left-censored  =          0
        upper = 100                                Right-censored =          0

                                                LR chi2(1)        =      14.17
                                                Prob > chi2       =     0.0002
Log likelihood = -17.655121                     Pseudo R2         =     0.2864

---------------------------------------------------------------------------------
       catholic |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        1.group |          5   .8944272     5.59   0.000     2.976665    7.023335
          _cons |          3   .6324555     4.74   0.001     1.569286    4.430714
----------------+----------------------------------------------------------------
 var(e.catholic)|          2   .8944272                      .7272243    5.500366
---------------------------------------------------------------------------------

.

When other predictors are present, as usually, the wording needs to mention them.

[Nora Ross]

Thank you for your explanation. Something that is confusing me is the fact that Catholics did not make up the majority in any county, so why are all the coefficients for the county variables positive? If they are the minority, shouldn't that result in negative coefficients?

[Nick Cox]

Again, the example I manufactured shows the logic.

Here the intercept is 3 which is the prediction when all the predictors are 0 (the prediction if group is 0) and the coefficient of the predictor is 5, taking the prediction 3 + 5 = 8 for group 1.

50% is not a reference level for anything here. Why should it be?