Backwards stepwise regression code in R (using cross-validation as criteria)
Your code is good. I could not find important corrections to be made. I could find only some small cosmetic improvements - nothing serious.

For example. You do not need the caret package loaded for this task. You do not need to use next at the end of the while loop. It is good practice to keep your code in width of 80 characters. It improves readability a lot. See my code attached.

rm(list=ls())
gc()

library(forecast)
library(fpp)

set.seed(1)
x1 &lt;- c(1:500) * runif(20, min=0, max=200)
x2 &lt;- c(1:500) * runif(20, min=0, max=200)

data(credit)
score &lt;- credit$score 
log.savings &lt;- log(credit$savings+1)
log.income &lt;- log(credit$income+1)
log.address &lt;- log(credit$time.address+1)
log.employed &lt;- log(credit$time.employed+1)


################################## 

#Input
full.model &lt;- score ~ log.savings + log.income + log.address +
  log.employed + x1 +x2


# 1. Start with the full model 
counter &lt;- 1L
full &lt;- lm(full.model)

scopevars &lt;- attr(full$terms, "predvars") # list of model predicotrs
n &lt;- length(full$residuals)  # sample size
current_best &lt;- full #what is the currenly the best model?
 # that would be our full model for now

while(T) { #process until we break the loop

  best_cv &lt;- CV(current_best)[1] #the CV of the current_best model
  temp &lt;- summary(current_best) #summary output of the current_best model 
  p &lt;- dim(temp$coefficients)[1]  # current model's size

  rnames &lt;- rownames(temp$coefficients)  # list of terms in the current model

  compare &lt;- matrix(NA,p,1) # create a matrix to store CV information 
  rownames(compare) &lt;- rnames #name the matrix 

  # create a loop that drops one predictor at a time and calculates
  # the CV of the regression when that predictor is dropped 
  # put all the information into "compare"
  # drop the variable that has the lowest CV when it is dropped.

  for (i in 2:p) { 
    drop_var &lt;- rnames[i] #variable to be deleted 
    f &lt;- formula(current_best) #current formula 
    f &lt;- as.formula(paste(f[2], "~", paste(f[3], drop_var, sep=" - ")))
    # modify the formula to drop the chosen variable (by subtracting it)
    new_fit &lt;- lm(f)  # fit the modified model 
    compare[i] &lt;- CV(new_fit)[1]
  }

  remove_var &lt;- rownames(compare)[which.min(compare)]
  # drop is the varibale that is associate with the lowest CV
  update_cv &lt;- compare[which.min(compare)]

  if (update_cv &gt; best_cv) break # we should not continue
  # if dropping a variable will not improve CV

  write(paste("--- Dropping", counter, remove_var , update_cv, "\n"), file="")
  # output the variables we are dropping

  f &lt;- formula(current_best) #current formula
  f &lt;- as.formula(paste(f[2], "~", paste(f[3], remove_var , sep=" - ")))
  # modify the formula to drop the chosen variable (by subtracting it)
  current_best &lt;- lm(f) # we now have a new best model
  counter &lt;- counter + 1L # update our counter
} #end the while loop 

print(current_best)
CV(current_best)