Dear all,

I am trying interpret the coefficient of logistic regression results and would very much appreciate if you could double-check my thinking on the steps below.

Dependent variable is pass (dummy: passed/not passed).
Motivation is a continuous variable between 0-100, tenure is also continuous (# years) and gender (1: male) and education (1: good university) are dummies.

Code:
logit pass motivation tenure i.gender_male i.edu
HTML Code:
Logistic regression                               Number of obs   =       9777
                                                  LR chi2(4)      =      62.17
                                                  Prob > chi2     =     0.0000
Log likelihood = -5551.7018                       Pseudo R2       =     0.0056

-------------------------------------------------------------------------------
         pass |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
   motivation |  -.0021914   .0012533    -1.75   0.080    -.0046479    .0002651
       tenure |  -.0174614   .0026707    -6.54   0.000     -.022696   -.0122268
1.gender_male |   .1047808   .0992882     1.06   0.291    -.0898205    .2993821
        1.edu |    .233494   .0528765     4.42   0.000      .129858    .3371301
        _cons |  -1.041527   .1336965    -7.79   0.000    -1.303568    -.779487
-------------------------------------------------------------------------------
From the regression output, I would like to interpret the coefficient of motivation and express the result in the following ways:

a) A one unit increase in motivation score, decreases the odds of passing by X %.
First, turn coefficient into an odds ratio: e(-0.002) = 0.998
My understanding of the interpretation is that a one unit increase in motivation score would decrease odds of pass by 0.002% "One unit" in my understanding refers to an increase from 0 to 1 on a scale of 0-100.

b) A 10% increase in motivation score, decreases the odds of passing by X %.
e(-0.002 * 1.1) = 0.997
Interpretation: A 10% increase would decrease odds of pass by 0.003%.

Does this make sense so far?

c) An increase in motivation score by one standard deviation, decreases the odds of passing by X %.
I am not sure how to approach this one - do you have any guidance?


One further question:
Coefficients for motivation are very small as shown in the regression output above. My understanding is that this is due to the scaling of the variable between 0-100. When rescaling the variable to 0-1, coefficients and effect sizes increase by x100:

Code:
logit pass motiv_100 tenure i.gender_male i.edu
HTML Code:
Logistic regression                               Number of obs   =       9777
                                                  LR chi2(4)      =      62.17
                                                  Prob > chi2     =     0.0000
Log likelihood = -5551.7018                       Pseudo R2       =     0.0056

-------------------------------------------------------------------------------
         pass |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    motiv_100 |  -.2191368   .1253341    -1.75   0.080    -.4647872    .0265136
       tenure |  -.0174614   .0026707    -6.54   0.000     -.022696   -.0122268
1.gender_male |   .1047808   .0992882     1.06   0.291    -.0898205    .2993821
        1.edu |    .233494   .0528765     4.42   0.000      .129858    .3371301
        _cons |  -1.041527   .1336965    -7.79   0.000    -1.303568    -.779487
-------------------------------------------------------------------------------
Repeating step a), this would imply:
e(-0.21) = 0.81
Interpretation: A one unit increase in motivation score would decrease the odds of pass by 19%.
My understanding is that in this case, "one unit" reflects an increase from the minimum score (0) to the maximum score (1) and that's why the effect size is 100x that above. Is that correct?

Thank you very much in advance again for your help!