# Thread: Log-transforming Only the Dependent Variable

1. ## Log-transforming Only the Dependent Variable

For the regression:
ln(gestation) = 5.28 + 0.0104×Birthweight

For the birthweight and gestation data, Minitab tells us that coefficient of birthweight(b1) = 0.01041.

minitab output:

and therefore:

exp(b1)=exp(0.010410)=1.01

The result tells us that the predicted median gestation changes by a factor of 1.01 for each one unit increase in birthweight. And for a 10-unit increase, median gestation changes by (1.01)^10 = 1.105 times.

My question:
For the reverse, does it mean that median gestation (changes) reduces by a factor of exp(0.010410)^(-1)=0.9896 for each unit decrease in birthweight? And for a 10-unit decrease, median gestation changes by exp(0.010410)^(-10)=0.9011 times?

2. ## Re: Log-transforming Only the Dependent Variable

Sorry for the delay - your post was held up by our spam software (it can get antsy for posts including attachments from new members!)

3. ## Re: Log-transforming Only the Dependent Variable

Length of gestation? Seems right. Don't have to exp, in no exp DV as percentage. I would multiply coefficient before back-transforming, is there a difference in solution doing it that way - can't remember my power rules?

4. ## Re: Log-transforming Only the Dependent Variable

Isn't it more natural to think about the birth weight as the dependent variable and the gestation period as the explanatory variable?

But what is the question in post 1?

5. ## Re: Log-transforming Only the Dependent Variable

That is what I was trying to get at as well!

6. ## Re: Log-transforming Only the Dependent Variable

Thanks for the response so far, no worries about the delay admin

I have rephrased the question in the first post of this thread. Usually when we relate to regression coefficients of the independent variables, we would be looking to describe "per unit increase of the independent variable, how much would the dependent variable change", I am wondering if my assumption of the "amount of change in the independent variable per unit decrease in the dependent variable"

7. ## Re: Log-transforming Only the Dependent Variable

Originally Posted by hlsmith
Length of gestation? Seems right. Don't have to exp, in no exp DV as percentage. I would multiply coefficient before back-transforming, is there a difference in solution doing it that way - can't remember my power rules?
Do you mind given an example with numbers?

8. ## Re: Log-transforming Only the Dependent Variable

A 1 unit increase in birth weight results in an expected 0.0104% increase in gestation. There is a fabulous article in "Epidemiology" that breaks down the use of log transformations. I think circa 2015.

Also for reference, just exponentiating the coefficient is an approximation, which I believe pretty much holds if the coefficient is 0.1 or less. Just for future endeavors, there is a more precise formula.

9. ## Re: Log-transforming Only the Dependent Variable

Originally Posted by hlsmith
A 1 unit increase in birth weight results in an expected 0.0104% increase in gestation. There is a fabulous article in "Epidemiology" that breaks down the use of log transformations. I think circa 2015.

Also for reference, just exponentiating the coefficient is an approximation, which I believe pretty much holds if the coefficient is 0.1 or less. Just for future endeavors, there is a more precise formula.
Hi hlsmith, taking 100*coefficient is the approximation usually for coefficients less than 0.1, 100*[exp(coefficient)] is the exact estimation that I have employed above. Please correct me if I am wrong.

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

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