I have a data frame like this
   df <- data.frame(tiny = rep(letters[1:3], 20), 
                  block = rnorm(60), tray = runif(60, min=0.4, max=2),
                  indent = sample(0.5:2.0, 60, replace = TRUE))
I nested this data frame
nm <- df%>%
       group_by(tiny)%>%
       nest()
then wrote these functions
library(dplyr)
library(purrr)
library(tidyr)
model <- function(dfr, x, y){
             lm(y~x, data = dfr)
         }
model1 <- function(dfr){
           lm(block~tray, data = dfr)
          }
I want to run this model for all tiny classes, so I did
 nm%>%
   mutate(
     mod = data %>% map(model1)
   )
the above code works fine but if I want to supply the variables as arguments like I have in the model1 function, I get errors. This is what I do      
 nm%>%
    mutate(mod = data %>% map(model(x=tray, y=block)))
I keep getting the error
Error in mode(x = tray, y = block) : unused argument (y = block). 
Also I tried plotting these using ggplot2 
plot <- function(dfr, i){
    dfr %>%
    ggplot(., aes(x=tray, y=block))+
geom_point()+
xlab("Soil Properties")+ylab("Slope Coefficient")+
ggtitle(nm$tiny[i])
nm%>%
 mutate(put = data %>% map(plot))
the idea is that I want ggplot to put titles a, b, and c for each of the plots that will be produced. 
Any help would be greatly appreciated. Thanks  
use base function split to split data into  list of groups.
library( purrr )
library( ggplot2 )
df %>% 
  split( .$tiny) %>%
  map(~ lm( block ~ tray, data = .))
df %>% 
  split( .$tiny) %>%
  map(~ ggplot( data = ., aes( x = tray, y = block ) ) +
        geom_point( ) +
        xlab("Soil Properties") + 
        ylab("Slope Coefficient") +
        ggtitle( as.character( unique(.$tiny) ) ) )
Using Functions:
lm_model <- function( data ) 
{
  return( lm( block ~ tray, data = data ) )
}
plot_fun <- function( data )
{
  p <- ggplot( data = data, aes( x = tray, y = block ) ) +
    geom_point( ) +
    xlab("Soil Properties") + 
    ylab("Slope Coefficient") +
    ggtitle( as.character( unique(data$tiny) ) )
  return( p )
}
df %>% 
  split( .$tiny) %>%
  map(~ lm_model( data = . ) )
df %>% 
  split( .$tiny) %>%
  map(~ plot_fun( data = . ) )
Creating formula inside function
lm_model <- function( data, x, y ) 
{
  form <- reformulate( y, x )
  return( lm( formula = form, data = data ) )
}
df %>% 
  split( .$tiny) %>%
  map(~ lm_model( data = ., x = 'tray', y = 'block' ) )
Your solution would have worked if you had your function formulated like below.
model <- function(dfr, x, y){
  lm( formula = eval(parse(text = paste('as.formula( ', y, ' ~ ', x, ')', sep = ''))),
      data = dfr)
}
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