# interpreting results of a log-linear regression [duplicate]

I am running a log-linear regression model, using the Fatalities data set, where estimated regression is an outcome variable (Fatalities) and contains fixed effects for the year and state. I am taking the log transformation of the Fatalities variable (numeric number of vehicle fatalities and have a question on 1) the interpretation of the coefficient on year and 2) the units of the residuals.

I want to correctly interpret a unit change in X on Y, where here X is year and Y is Fatalities. I have taken the exponent of the coefficient of year (X) and found the percentage change. For example, from 1983 compared to 1982, a unit change in X is associated with a 1-0.97 = 0.03 percent reduction in fatalities. Is this correct?

A second question is related to the residuals, that is the difference between the predicted and observed values of Y (Fatalities). Are the residuals in the original units of Y (Fatalities per year) or some log-transformed units of Y?

 library(AER)
data("Fatalities")

lm.fatalities <- lm(log(fatal) ~ factor(year) + factor(state), data = Fatalities)
summary(lm.fatalities)

Call:
lm(formula = log(fatal) ~ factor(year) + factor(state), data = Fatalities)

Residuals:
Min       1Q   Median       3Q      Max
-0.28200 -0.03741  0.00472  0.04371  0.34215

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)       6.86469    0.03572 192.202  < 2e-16 ***
factor(year)1983 -0.02754    0.01819  -1.514 0.131098
factor(year)1984 -0.01049    0.01819  -0.577 0.564537
factor(year)1985 -0.02083    0.01819  -1.145 0.253022
factor(year)1986  0.03161    0.01819   1.738 0.083312 .
factor(year)1987  0.03625    0.01819   1.993 0.047190 *
factor(year)1988  0.05334    0.01819   2.933 0.003633 **
[state factors hidden]
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef(lm.fatalities))
(Intercept) factor(year)1983 factor(year)1984 factor(year)1985 factor(year)1986
957.8494564        0.9728391        0.9895654        0.9793859        1.0321105
factor(year)1987 factor(year)1988  factor(state)az  factor(state)ar  factor(state)ca
1.0369148        1.0547858