In this article in the section of "Logistic regression with multiple predictor variables and no interaction terms" is stated:

This fitted model says that, holding math and reading at a fixed value, the odds of getting into an honors class for females (female = 1)over the odds of getting into an honors class for males (female = 0) is exp(.979948) = 2.66. In terms of percent change, we can say that the odds for females are 166% higher than the odds for males.

How was the value of 166% calculated? It seems that the author just subtracted 1 from 2.66 and multiplied by 100% but according to which formula?


1 Answer 1


When the odds are 1, this means males and females are just as likely of getting into an honor class. So when the odds are 1+1 = 2, this means the odds are now twice as likely or a 100% increase in odds (from 1 to 2). So, you'll need to subtract 1 from the odds to obtain the percent increase. So in your example the odds are 2.66 (going from 1 to 2.66 means the odds increased by 2.66-1 = 1.66. This means that there is a 166% increase in the odds ($2.66-1)\times100$%). If the odds were less than 1, it would not be a percent increase, but a decrease. For example if the odds were .97, then that would mean there was a 1-.97 = .03 or 3% reduction in the odds.

To look at this another way, think of it like this. If I have 100 cupcakes and then make 25 more, than I have increased the the number of cupcakes by 25%, or I have produced $\frac{{125\mbox{ cupcakes}}}{{100\mbox{ cupcakes}}} = 1.25$ times as many cupcakes ($1.25 \times 100$ original cupcakes = 125 cupcakes). The "1" in front of the ".25" implies an increase.

This is essentially just basic arithmetic.

You might find these other posts helpful too: Interpretation of the regression coefficient of a proportion type independent variable


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.