Interpreting categorical coefficients

In your Bayesian model, \(m\)_i \(= a + b X\)_i specified the dependence of typical trail volume on weekday status \(X\)_i (1 for weekdays and 0 for weekends). A summary() of your RJAGS model simulation provides posterior mean estimates of parameters \(a\) and \(b\), the latter corresponding to b.2. here.

> summary(rail_sim_1)
       Mean     SD Naive SE Time-series SE
a    428.47 23.052  0.23052         0.5321
b.1.   0.00  0.000  0.00000         0.0000
b.2. -77.78 27.900  0.27900         0.6422
s    124.25  9.662  0.09662         0.1335

Which of the following is the best interpretation of these posterior summaries?

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Possible Answers

Typically, there are 428.47 trail users on a weekday and 77.78 fewer users (~350.69) on a weekend day.
press1
Typically, there are 428.47 trail users on a weekend day and 77.78 fewer users (~350.69) on a weekday.
press2
Typically, there are 428.47 trail users on a weekday and only -77.78 users on a weekend day.
press3
Typically, there are 428.47 trail users on a weekend day and only -77.78 users on a weekday.
press4