R: apply function per group using dplyr

Question

I have a function which detrends data:

detrender <- function(Data,Vars,timevar){
  Data_detrend <- Data
  for (v in seq_along(Vars)){
    ff <- as.formula(paste0(Vars[[v]]," ~ ",timevar))
    fit <- lm(ff, data = Data_detrend)
    if (anova(fit)$P[1] < 0.05){
      message(paste("Detrending variable",v))
      Data_detrend[[Vars[v]]][!is.na(Data_detrend[[Vars[[v]]]])] <- residuals(fit)
    }
  }
  Data_detrend
}
useVar <- c("depression_sum")
inertia <- detrender(inertia,useVar, "timestamp")

This works fine, and detrends my data. However, as my datafile has many groups (Rid), detrend is conducted across groups. I want to detrend per group (Rid) and have tried to apply my function using group_by in dplyr. However, this code seems to add thousands of new rows with data. This is wrong, the number of rows should stay the same, while the data is detrended.

inertia_2<- inertia %>% 
  group_by(Rid) %>%
  do(detrender(inertia,useVar, "timestamp")) %>%
  ungroup()