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I have a following OLS regression model

log(y) = a + b*x_1 + c*x_2 + d*log(x_3) + error

I am now wondering what is the interpretation of the coefficient d- is it that one unit change in log(x_3) causes d units change to the log(y)? Are there any extra consequences of one independent variable being log transformed that I should be aware of?

Many thanks!

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  • $\begingroup$ Hi: For every 1 percent change in x_3, there is a d percent change in y. It seems a little odd to me transform one of the independent variables but not the others. When I say, "odd:, I mean that it's a little strange that one would work better using the log scale and the others wouldn't need it ? But that would depend on the meanings of the variables. I'm not sure about other consequences but I don't know of any. $\endgroup$
    – mlofton
    May 30, 2021 at 14:34

1 Answer 1

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If you change the variable x_1 to x_1 + 1 and keep all the other variables the same, then you have odd_post/odd_pre = exp(beta1), since you have log(y) = beta_ix_i => y = exp(beta_ix_i) and all the other terms cancel.

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