# Log-transformed DV and coefficient of interaction term

I am having difficulty interpreting the significance of positive tone (measured as percentage of words in a sentence that are positive in tone) for females and males. The following is the regression estimate for the log-transformed dependent variable.

log(DaysToOutcome)=-0.12 -0.32*Female + 0.02*PositiveTone +0.03*NegativeTone -0.04*Female:PositiveTone -0.03*Female:NegativeTone.


How do I estimate what one percentage point change in positive tone would result in terms of percentage change in outcome variable for females and males? Please help!

Let $$X$$ = positive tone percent, $$Z$$ = negative tone percent, $$Y$$ = daystooutcome. For male with $$X = x$$, $$log(Y|x) = -0.12 +0.02x +0.03Z$$. For male with $$X=x+1$$ (one percentage point change), $$log(Y|x+1) = -0.12 +0.02(x+1) +0.03Z$$. So $$log(Y|x+1) - log(Y|x) = log\left(\frac {Y|x+1}{Y|x}\right) = 0.02$$. So $$\frac {Y|x+1}{Y|x} = e^{0.02}$$ for male.

For female, we have $$log(Y|x) = -0.12 -0.32 + 0.02x - 0.03Z -0.04x$$.

$$log(Y|x+1) = -0.12 -0.32 + 0.02(x+1) - 0.03Z -0.04(x+1)$$.

$$log(Y|x+1) - log(Y|x) = log\left(\frac {Y|x+1}{Y|x}\right) = 0.02 - 0.04 = -0.02$$.

$$\frac {Y|x+1}{Y|x} = e^{-0.02}$$ for female.

• Thanks a lot @a_statistician!! Would that mean for females 1 percent increase in X (i.e., PositiveTone) would lead to (exp(-0.02)-1)*100 change in Y (i.e., DaysToOutcome)? Commented Oct 17, 2018 at 2:44
• I think you should understand what $\frac {Y|x+1}{Y|x} = e^{-0.02} = 0.98$ means. The rest is language issue. It is really beyond my ability. Commented Oct 17, 2018 at 2:51
• Also another clarification, would a 50 percent increase in positive tone, mean (exp(50*-0.02)-1)*100 percent change in days to outcome for females? Am I getting this correct? Please correct me if I am wrong. Commented Oct 17, 2018 at 2:51
• One question for you: when you fit model, if positive tone percent is 10%, you used 10 or 0.10? If you used 10, then everything we discussed are OK. If you used 0.10, we need to recalculate them. Commented Oct 17, 2018 at 2:56
• $\frac {Y|x+50}{Y|x} = e^{-0.02*50} = e^{-1} = 0.3679$ for female with a 50 percent increase in positive tone. Commented Oct 17, 2018 at 3:01