You can use the matrix form to do this:
logitp_est <- sum(c(1, values) * coefficients)
If you want the probability,
prob_est <- 1 / (1 + exp(-1 * logitp_est))
or the built in plogis()
:
prob_est <- plogis(logitp_est)
If you want the classification:
class_est <- logitp_est > 0