# Interpret GLM log link coefficients

I am currently doing a college assignment in which I have a GLM model in the gaussian family with a log link. I would like to know what the impact per variable is. I know how to calculate the predicted values per observation, but I would like to make claims like "with every unit increase in x, y increases by 3%". The output of my model is pasted below.

Call:
glm(formula = Autodate % ~ Population density + Parking rate +
Waiting time + Green party % +Dutch % + West % +
Average income, family = gaussian(link = "log"), start = c(0,
0, 0, 0, 0, 0, 0, 0))

Deviance Residuals:
Min        1Q    Median        3Q       Max
-0.46555  -0.06470  -0.00322   0.09149   0.48983

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)          -3.624336   0.496889  -7.294 2.16e-10 ***
Population density  0.001094   0.000271   4.035 0.000127 ***
Parking rate       -2.180515   0.289239  -7.539 7.32e-11 ***
Waiting time        0.067415   0.014370   4.691 1.14e-05 ***
Green party %       0.049266   0.008311   5.928 7.89e-08 ***
Dutch %             0.012612   0.005018   2.514 0.014012 *
West %              0.022385   0.006857   3.265 0.001629 **
Average income      0.020760   0.003403   6.100 3.83e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.02706026)

Null deviance: 22.9258  on 85  degrees of freedom
Residual deviance:  2.1107  on 78  degrees of freedom
AIC: -56.773

Number of Fisher Scoring iterations: 8

• Can you paste in your output? – gung Jun 3 at 16:57
• I have added my output to my question – KlaasR Jun 3 at 17:25
• Possibly related? stats.stackexchange.com/questions/18480/… – AdamO Jun 3 at 17:36
• @adamO your linked question is asking about the a linear model with a log-transformed outcome. Will that have the same interpretation as the normal GLM with a log link? – Great38 Jun 3 at 17:50
• From names it seems that you have a response that is a percent and are using a log link. That could work fairly well if and only if all the values are much closer to 0 than to 100 (or to 1 if despite the name the response is measured as a proportion). Otherwise a logit link is a better idea for such a response. – Nick Cox Jun 3 at 18:02