AIM: To really, really understand what the model outputs mean in a log-linear regression, specifically, how to interpret the residual standard error (RSE).
I have read this post but it does not specifically address RSE for log-linear models.
This is the log-linear model:
lm(formula = log(n_capita) ~ edu_index_percent, data = full_maps_edu)
So far, to my understanding I know that the RSE is the average amount that the response will deviate from the true regression line. Great. But because I have logged the dependent variable, can I say:
n_capitawill deviate on average about 1.33 from the true regression line?
I think that should't make sense because the response variable is logged. Should it instead be:
n_capitawill deviate on average about $e^{1.33}$ from the true regression line?
I'm a bit confused. Please advise.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -9.92029 0.38053 -26.1 <0.0000000000000002 ***
edu_index_percent 0.10345 0.00592 17.5 <0.0000000000000002 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.33 on 167 degrees of freedom
Multiple R-squared: 0.646, Adjusted R-squared: 0.644
F-statistic: 305 on 1 and 167 DF, p-value: <0.0000000000000002
