I ran a mixed model regression and obtained the following output. Because I log-transformed the concentration variable, I interpreted the coefficient as follows: the mean concentration is reduced $1.5$ percent each year. The years run from 1993-2010.

Can say also state that the mean concentration is reduced by $26\%$ ($0.01509\cdot 17$) over the $17$ year period? Why or why not?

Why do most people generally state $1$ unit increase in $X$ corresponds to a certain number change in $Y$ rather than infer change over the entire period?

baggerTrend <-  lme(Log.Qconc   ~   Yearf,  random=(~Yearf|MineID), Bagger) 

Random  effects:                    
    Formula:    ~Yearf  |   MineID      
    Structure:  General positive-definite,  Log-Cholesky    parametrization 
              StdDev    Corr                
(Intercept) 0.209172851 (Intr)              
Yearf       0.000374953 -0.478              
Residual    0.785367538                 

Fixed effects:  Log.Qconc ~ Year                    
               Value   Std. Error    DF      t-value       pvalue
Intercept   33.71122    6.3901     2762      5.275538       0
Year        -0.01509    0.003193   2762     -4.724678       0
  • $\begingroup$ If your dependent variable in the analysis is log-transformed concentration, then the coefficient for year is telling you that log-transformed concentration decreases by 0.015 every year, the coefficient is on the same scale as your DV, which is not percentages in this case. $\endgroup$
    – Marius
    Commented Jul 12, 2012 at 1:38
  • $\begingroup$ Also, if you did not mean-center Year, and used values like 1993, 1994, etc., then the coefficients may be nonsensical, because the model is fitted for year==0. $\endgroup$
    – Marius
    Commented Jul 12, 2012 at 1:40
  • $\begingroup$ @Marius: I interpreted the percent change/decrease based on information from this website: ats.ucla.edu/stat/sas/faq/sas_interpret_log.htm. I am 90% sure but I can be wrong. $\endgroup$
    – Amateur
    Commented Jul 12, 2012 at 4:06
  • 1
    $\begingroup$ Just had a quick look, and found this: sportsci.org/resource/stats/logtrans.html. Log-transformed coefficients do closely approximate percentages, but only when they are small. $\endgroup$
    – Marius
    Commented Jul 12, 2012 at 4:44
  • 1
    $\begingroup$ @Amateur so your question is about the interpretation of a regression line and has nothing to do with the mixed model ? $\endgroup$ Commented Jul 12, 2012 at 5:03

1 Answer 1


I think that would be enough to consider exp coefficient and interpret it this way: the unit change of the regressor x1, creates an increase of exp (b1) of the dependent variable

  • $\begingroup$ Can you expand on this as it does not seem to add very much to the comments? $\endgroup$
    – mdewey
    Commented Nov 16, 2016 at 15:53
  • $\begingroup$ {\displaystyle \log(Y)=a+bX} \log(Y)=a+bX {\displaystyle Y=e^{a}e^{bX}} Y=e^{a}e^{{bX}}) $\endgroup$ Commented Nov 16, 2016 at 17:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.