How Do I Generate All Possible Combinations of the Variables In A Model In R?

Question

Assuing I have a table with several variables, a - h , where h is the target/y/predicted variable:

a <- rnorm(10,5,1)
b <- rnorm(10,5,1)
c <- rnorm(10,5,1)
d <- rnorm(10,5,1)
e <- rnorm(10,5,1)
f <- rnorm(10,5,1)
g <- rnorm(10,5,1)
h <- rnorm(10,5,1)

df = data.frame(a,b,c,d,e,f,g,h)

I want to run the AIC to determine the best possible model for predicting h . To do that, I need to run every single combination of df[1:7] . So I'd need the AICs of:

lm(fomula= h ~ a+b+c+d+e+f+g)
lm(fomula= h ~ a+b+c+d+e+f)
lm(fomula= h ~ a+b+c+d+e)

As well as every other configuration of the variables. Is there any way I can do this please?

To get every possible formulation of the variables I've tried:

library(combinat)
combn(colnames(df[,1:7]))

However, I only got:

[1] "a" "b" "c" "d" "e" "f" "g"

As the output of the above code which is a far cry from what I ultimately want.

Answer 1

use the step function. This should give you the best model:

step(lm(h~., df),direction = 'both', trace = 0)

Call:
lm(formula = h ~ b + e + f, data = df)

Coefficients:
(Intercept)            b            e            f  
     4.3494      -0.8705      -0.3266       1.2877  

This model has the lowest AIC . You can change trace = 1 , to look at the intermediate models that were run