Log transformed variables in linear Regression

[Alex Hartley]

Hi guys,

I am not too experienced with statistics, but am conducting some quantitative analysis for my undergrad Psychology dissertation and would like a bit of help please.

I ran a linear regression to see if social support level (a binary variable - either low or high) could predict Total Difficulties Score (a continuous variable). But, when running my assumptions test, the assumption of homoscedasticity was violated. Therefore, I did some research and found that one way of overcoming this problem is by log transforming the dependent variable. So, I log transformed Total difficulties score, creating a new variable called log_totaldifficultiesscore. I then reran the regression and the assumption was no longer violated, so the problem was overcome. BUT, I am know unsure as to HOW to interpret the coefficients, as it is no longer RAW scores being discussed in the regression but LOG TRANSFORMED SCORES. So, what would a coefficient of -.370 actually mean? Or, how can I can I 'un-log transform' the coefficients??

I hope my explanation makes sense and someone can help, I have been struggling with this for a few days now!

Thank you

[Clyde Schechter]

So, if Y0 is the value of total difficulties when social support == 0, and Y1 is the value of total difficulties when social support = 1, we have the following equations:

log(Y1) - log(Y0) = coefficient of social support = -0.370
==>
log Y1 = log Y0 - 0.370
==>
Y1 = Y0 * exp(-.370) = Y0 * 0.691

In words, the effect of social support on total difficulties is reduction by a factor of 0.691. This could also be said as a percentage reduction of 100*(1-0.691) = 30.9%.