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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
KlaasR
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    Can you paste in your output? – gung - Reinstate Monica Jun 03 '19 at 16:57
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    I have added my output to my question – KlaasR Jun 03 '19 at 17:25
  • Possibly related? https://stats.stackexchange.com/questions/18480/interpretation-of-log-transformed-predictor-and-or-response/ – AdamO Jun 03 '19 at 17:36
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    @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? – Michael Webb Jun 03 '19 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 03 '19 at 18:02
  • @Great38 yes. The log link is the same as long transform in terms of the mean model and interpretation of coefficients. The variance structure (the other aspect of GLM) doesn't affect the estimator's value, just the efficiency of the inference. – AdamO Jun 03 '19 at 18:18
  • Thanks for your replies! I'm not sure what is meant by a percent increase. A percent increase from what? – KlaasR Jun 03 '19 at 18:27
  • Can you say more about what your data are? What is "Autodate %"? Is this a number of times something happened out of the number of times it could have happened? What are the other variables? What is the point of fitting this model? – gung - Reinstate Monica Jun 03 '19 at 19:17
  • The "Autodate %" is the percentage of car sharing spaces on the total number of parking spaces per Amsterdam neighbourhood. The other variables are characteristics per neighbourhood who I am using to find out how they impact the Autodate %. – KlaasR Jun 03 '19 at 19:34

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