Average of root mean square error Is taking the average of different rmse valid? for example 
                  average rmse = (rmse1+rmse2+rmse3)/3
Thank you for your help!
 A: I actually wasn't sure about this either so I tested it out with a short example:
## Create simple function to calcualte the error
rmse <- function(error){sqrt(mean(error^2))}

## Define two example error vectors
error1 <- c(0.4, 0.2, 0.01)
error2 <- c(0.1, 0.3, 0.79)

## Find the RMSE of each error vector
rmse1 <- rmse(error1)
rmse2 <- rmse(error2)

## Compare the RMSE variants
print(rmse_all <- rmse(c(error1, error2)))
[1] 0.3924708
print(rmse_avg <- mean(rmse1, rmse2))
[1] 0.2582634

So we can se that they are not equal.
## As described by @whuber in the comments:
                                                 
a <- rmse1^2*length(error1)                 # - square each rmse & multiply
b <- rmse2^2*length(error2)                 #   it by its associated count
c <- sum(a, b)                             # - sum that stuff up,                  
d <- c/sum(length(error1), length(error2))   # - divide by the total count,          
print(total_rmse <- sqrt(d))               # - take the square root.
[1] 0.3924708

