Interpretation log-log regression

[Pita Fouta]

Hello everyone,

Would anyone know how I could interpret the log-log regression with age below?

ln (Income) = const + 0.30 ln(Age) + ut

I don't understand how it is possible to say that if age increases by 1%, income increases by 30%. Age is a unit (count), you can't age by 1% that's why I have trouble interpreting it.

Thanks in advance

Pita Fouta

[Nick Cox]

It's possible to say that, but no one is doing that and it's not what the regression means. 0.30 or 30% is the gradient ln(Income) / ln(Age) which means that a unit increase in ln Age means a 0.3 increase in ln(Income)

[Pita Fouta]

Thanks a lot Nick Cox . I had understood that for log log regressions, you had to say that a 1% increase in age results in a 0.3 increase in income. But then according to your answer, how can I interpret the regression? By saying that an increase of one unit of age (so one year more), the income increases by 0.3, even if both variables have a logarithm? Thanks in advance and sorry if my question sounds naive.

[Nick Cox]

I don't have a different answer to offer beyond underlining that this fit on logarithmic scale (i.e. a power function fit) is not linear on the original scale. Perhaps you need to revise logarithms.

Cross-posted at https://stats.stackexchange.com/ques...count-variable

[Carlo Lazzaro]

Pita:
absit iniuria verbis (about dummies, I mean) you may want to take a look at:
https://www.dummies.com/article/busi...g-model-156386