Automatically select best columns for best subset

The Leaps package allows identification of subsets, and can return results for the best subsets. For example:

library(leaps)
mtcars.regsubsets <- regsubsets(mpg ~ ., data = mtcars)
summary(mtcars.regsubsets, nvmax = 10)

Selection Algorithm: exhaustive
         cyl disp hp  drat wt  qsec vs  am  gear carb
1  ( 1 ) " " " "  " " " "  "*" " "  " " " " " "  " " 
2  ( 1 ) "*" " "  " " " "  "*" " "  " " " " " "  " " 
3  ( 1 ) " " " "  " " " "  "*" "*"  " " "*" " "  " " 
4  ( 1 ) " " " "  "*" " "  "*" "*"  " " "*" " "  " " 
5  ( 1 ) " " "*"  "*" " "  "*" "*"  " " "*" " "  " " 
6  ( 1 ) " " "*"  "*" "*"  "*" "*"  " " "*" " "  " " 
7  ( 1 ) " " "*"  "*" "*"  "*" "*"  " " "*" "*"  " " 
8  ( 1 ) " " "*"  "*" "*"  "*" "*"  " " "*" "*"  "*" 

The summary gives an "*" for the best results for the number of columns. It's also possible to use a specific measure, such as Mallow's Cp to find the best result:

which.min(summary(mtcars.regsubsets)$cp)

3

This returns that conclusion that the 3-variable set has the lowest score for Mallow's Cp.

Is there a way to automatically select those columns (wt, sec and am in this case) in the data set, so it returns a new data set only with those three columns?

mtcars[,c(5,6,8)]

Obviously the help file for the Leaps package has been checked, looked on StackOverflow, other sources, but no solution was found.

Here is one way using dplyr:

library(leaps)
library(dplyr)
mtcars.regsubsets <- regsubsets(mpg ~ ., data = mtcars)

cols_sel <- mtcars.regsubsets |> 
  broom::tidy() |> 
  filter(mallows_cp == min(mallows_cp)) |> 
  select(where(~.x == TRUE)) |> 
  colnames()

select(mtcars, any_of(cols_sel))

You can use the summarys component "which" and scan its columns, row by row, for TRUE values, the retrieve the associated column = variable names and store it in a list. Then, you can pick the column names from this list, using the desired number of variables.

With base R:

column_sets <- 
  apply(
    regsubsets(mpg ~ ., data = mtcars) |>
    summary() |>
    (`[[`)('which'),
    MARGIN = 1,
    FUN = \(x) names(x)[x][-1] ## drop "(Intercept)"
  )

mtcars[column_sets[['3']]]

+ mtcars[column_sets[['3']]]
                       wt  qsec am
Mazda RX4           2.620 16.46  1
Mazda RX4 Wag       2.875 17.02  1
Datsun 710          2.320 18.61  1
Hornet 4 Drive      3.215 19.44  0
Hornet Sportabout   3.440 17.02  0
Valiant             3.460 20.22  0
Duster 360          3.570 15.84  0
## ...

Get the summary, it has a "which" matrix, get column sums excluding intercept, and get the columns with most TRUE values, using tail:

ss <- summary(mtcars.regsubsets, nvmax = 10)

names(tail(sort(colSums(ss$which[, -1 ])), which.min(ss$cp)))
# [1] "qsec" "am"   "wt"