"If desired, the confidence interval can then be transformed back to the original scale using the inverse of the transformation that was applied to the data."

]]>THANK you once again for creating this blog and for your help.

]]>If you plug in GENDER=0 with some set of X values into the equation, you get the fitted ln(Y) for women. Then plug in GENDER=1 with the same X values, you get the fitted ln(Y)for men. Note that ln(y) is not the geometric mean (you have to take an exponent to get the geometric mean). The difference between these fitted ln(y) numbers is the coefficient of GENDER.

Suppose the coefficient for GENDER is b_Gender. And y_women is the geometric mean for women.

Then (roughly speaking):

b_GENDER = ln(y_men)- ln(y_women)

and so:

exp(b_GENDER) = y_men / y_women

Hence, the exponent of the coefficient gives you the ratio of the geometric means of men and women.

Check out this newsletter, which uses the term "geometric mean". In particular, they explain:

"when we exponentiate the predicted value of ln(Y), we get the predicted geometric mean of Y rather than the predicted arithmetic mean".

http://www.cscu.cornell.edu/news/statnews/stnews83.pdf

Or the 'average percent difference' in the average, i.e. means of the two groups?

Thanks!

]]>If you compute a confidence interval for a beta parameter, then the CI will also need to be interpreted in the same manner. For a 90% CI, you'll say that you are 90% confident that the average percentage difference between women and men is… (all else constant).

The CI calculation is the same (it has nothing to do with which interpretation you use).

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