# How do I interpret the results of a log-linear regression involving constructed personality trait independent variables?

The following model was estimated:

Linear regression
Number of obs     =      1,027
F(45, 981)        =      17.85
Prob > F          =     0.0000
R-squared         =     0.4268
Root MSE          =     .46636
|               Robust
lunpaid |      Coef.   Std. Err.      t    P>|t|
ropen1 |   .0257707   .0140323     1.84   0.067
rextra1 |   .0208155   .0128139     1.62   0.105
ragree1 |   .0210167   .0175203     1.20   0.231
rcon1 |   .0494945   .0180238     2.75   0.006
rneur1 |   .0154446   .0133066     1.16   0.246


where lunpaid (the dependent variable) is equal to the log of unpaid overtime, and ropen1 - rneur1 correspond to the big 5 personality traits openness extraversion, agreeableness, conscientiousness and neuroticism. (A number of controls were included in the model however I have excluded them from the picture.) These independent variables were generated by taking an average of 3 likert measured traits from 'does not apply to me' to 'applies to me perfectly'.

   big5: forgiving nature   |      Freq.     Percent        Cum.
----------------------------+-----------------------------------
does not apply to me at all |         16        0.64        0.64
2 |         78        3.13        3.77
3 |        173        6.94       10.71
4 |        319       12.80       23.52
5 |        649       26.04       49.56
6 |        910       36.52       86.08
applies to me perfectly |        347       13.92      100.00
----------------------------+-----------------------------------
Total |      2,492      100.00

The average of forgiving nature + 2 more traits looks like this:

agree |      Freq.     Percent        Cum.
------------+-----------------------------------
2 |          3        0.04        0.04
2.333333 |         14        0.19        0.23
2.666667 |         33        0.44        0.66
3 |         78        1.03        1.70
3.333333 |         90        1.19        2.89
3.666667 |        161        2.14        5.03
4 |        233        3.09        8.12
4.333333 |        324        4.30       12.41
4.666667 |        490        6.50       18.91
5 |        675        8.95       27.86
5.333333 |        848       11.25       39.11
5.666667 |      1,117       14.81       53.93
6 |      1,304       17.29       71.22
6.333333 |      1,135       15.05       86.27
6.666667 |        554        7.35       93.62
7 |        481        6.38      100.00
------------+-----------------------------------


The age variable was then regressed on each generated personality variable and the residuals were used as the explanatory variables in the regression (in order to remove age effects).

My question is, how should I interpret the coefficients? I realise that conscientiousness is the only statistically significant result. Is this interpretation correct:

A unit increase in trait conscientiousness is associated with a 5% increase in unpaid overtime hours supplied, and this result is highly significant at the 1% level.

• Possible duplicate of Interpretation of log transformed predictor – gung Jan 11 '17 at 2:16
• Apologies for the images, I have edited my submission. I understand that the usual interpretation for a log-linear model is: "One unit increase in IV is associated with a (B1 * 100) percent increase in DV." I am wondering how this interpretation might change given how the independent variables were generated. – L.Emma Jan 11 '17 at 2:40
• I'm not sure I see how they were generated makes any difference to their interpretation. Can you say more? – gung Jan 11 '17 at 2:42
• @gung Sorry if I'm not explaining myself well. I have updated my post with one of the average of 3 traits (agreeableness) variable. I guess I'm just paranoid that using generating the variables from the likert scale changes the interpretation. I take it that this interpretation seems correct: A unit increase in trait conscientiousness is associated with a 5% increase in unpaid overtime hours supplied, and this result is highly significant at the 1% level. – L.Emma Jan 11 '17 at 12:07