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I have the following question: If I perform a logistic regression for "amount of fluid" (independent variable, unit is milliliters) and the outcome "pass = 1 vs. fail = 0" (as dependent variable) and receive the following results for b = 0.205 > so the odds ratio is 1.227 (EXP of 0.205).

Is it correct to say that:

  1. an increase of 1 milliliter of fluid results in an increase of odds for pass by 1.227 and this is equal to an increase by 22.7 percent
  2. a decrease of 1 milliliter of fluid results in a decrease of odds for pass by 0.814 (1 / 1.227) and this is equal to a decrease by 18.5 percent (1 - 1/1.227)

As one milliliter is of less interest than a change of 10 milliliters - is it correct to say that

  1. an increase of 10 milliliters of fluid results in an increase of odds for pass by 7.768 (1.227^10) and this is equal to an increase by 776.8 percent?

  2. a decrease of 10 milliliters of fluid results in a decrease of odds for pass by 0.127 (0.814^10) and this is equal to a decrease by 12.7 percent?

Another question is the following:

How do I interpret an OR < 1? By beta is "-0.009" (negative!) leading to an OR of 0.991. So how do I interpret this for

  1. an increase of 1 milliliter
  2. a decrease of 1 milliliter
  3. an increase of 10 milliliters
  4. a decrease of 10 milliliters

Thank you so much for any help! It would be really helpful for me if the answers use my numbers with the three digits so I can retrace them.

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  • $\begingroup$ Hi! Thank you for your reply. Unfortunately this does not answer my question as I need help with the interpretation of the values... But thank you for your support! $\endgroup$
    – MDStat
    Aug 18, 2021 at 9:03
  • $\begingroup$ If you have a multiplicative factor of $1.227$ as a $22.7\%$ increase, then a multiplicative factor of $7.768$ is a $676.8\%$ increase $\endgroup$
    – Henry
    Aug 18, 2021 at 9:17
  • $\begingroup$ $\exp(-0.991) \approx 0.37$ which as a multiplicative factor would be a $63\%$ decrease in the odds $\endgroup$
    – Henry
    Aug 18, 2021 at 9:19
  • $\begingroup$ Hi Henry! Thank you for your comments! I understand your first answer with 676.8%, thank you! I'm sorry, I made a mistake - you are right. I wanted to say that my beta is "-0.009" so the OR is 0.991. So does that mean a 89.5% decrease ((1-.991)*100) in the odds? $\endgroup$
    – MDStat
    Aug 18, 2021 at 9:45

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