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
