Binary Regression

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    I was hoping to get some assistance with the interpretation of binary logistic regression. 
    I have two factors, one continuous and the other is discrete.  Both are significant in terms of the response.  I understand the interpretation of the odds ratio for the continuous factor (for each additional unit it increases the percent of my response by 9%).  I’m not quite sure of the interpretation of the odds ratio for the discrete factor which is .27. 
    Is it also possible to build an equation for both factors for predicting the response?  This would be synonomous with writing the equation for a continuous response?
    Thanks for any advice.


    Ken Feldman

    Are you properly using the tool?  From what I understand, Binary logistic requires a discrete Y and a continuous X.  Didn’t see mention of the use of a discrete X.



    My response is discrete.  Minitab will allow you to include both continuous and discrete factors.



    You said>>continuous factor (for each additional unit it increases the percent of my response by 9%).
    I don’t know how did you come up with this statement? Did you make this statement because you got an odd ratio of .09 for your continuous variable? If that is the case then your statement (interpretation) is not correct. For interpreting this correctly we need the reference level of your response.
    Other information needed to answer this question, what is your Link function (You can see this at the top the session’s window). What are the reference levels, of both Y and X’s.
    It would be good if you can copy and paste the session’s window here.



    Here is my session window.  Both factors are discrete with two categories.
    Link Function: Logit
    Response Information
    Variable Value Count
    ams client yes 37 (Event)
    no 1745
    Total 1782
    Logistic Regression Table
    Odds 95% CI
    Predictor Coef SE Coef Z P Ratio Lower Upper
    Constant -3.82748 0.201771 -18.97 0.000
    pfp sent
    Y -1.65808 0.729752 -2.27 0.023 0.19 0.05 0.80
    Funded Cat
    >15 0.784532 0.366535 2.14 0.032 2.19 1.07 4.49
    Log-Likelihood = -173.818
    Test that all slopes are zero: G = 12.309, DF = 2, P-Value = 0.002
    Goodness-of-Fit Tests
    Method Chi-Square DF P
    Pearson 0.268379 1 0.604
    Deviance 0.253976 1 0.614
    Hosmer-Lemeshow 0.113079 1 0.737
    Table of Observed and Expected Frequencies:
    (See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)
    Value yes no
    Group Observed Expected Observed Expected Total
    1 1 1.3 322 321.7 323
    2 26 25.3 1206 1206.7 1232
    3 10 10.3 217 216.7 227
    Measures of Association:
    (Between the Response Variable and Predicted Probabilities)
    Pairs Number Percent Summary Measures
    Concordant 25477 39.5 Somers’ D 0.27
    Discordant 8198 12.7 Goodman-Kruskal Gamma 0.51
    Ties 30890 47.8 Kendall’s Tau-a 0.01
    Total 64565 100.0



    Thanks for pasting the sessions window.
    You might read /interpret the Odds ratio like this
    An AMS client who has Funded cat>15 has an Odds of 2.19 times larger of saying “Yes” than who has <15 Funded cat (On the assumption that the reference level for funded cat is 15.
    More AMS client who have pfp sent “Y” has said “No”. In other words, the AMS client  who have pfp “Y” said “Yes” is only 19% when compared to AMS client said “Yes” having pfp “N” (On the assumption that the reference level for pfp is “N”)
    Practically if you need AMS client “Yes” you might go with pfp “N”
    Hope this helps. Please let me know; also please consider English is not my first language. Besides I don’t know what these factors mean in practical :0.

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