You can use the regsubsets() function from the leaps package in R to find the subset of predictor variables that produces the best regression model.

The following example shows how to use this function in practice.

Example: Using regsubsets() for Model Selection in R

For this example we’ll use the built-in dataset in R, which contains measurements on 11 different attributes for 32 different cars.

#view first six rows of mtcars datasethead(mtcars)

                   mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

Suppose we would like to fit a regression model using hp as the response variable and the following potential predictor variables:

• mpg
• wt
• drat
• qsec

We can use the regsubsets() function from the leaps package to perform an exhaustive search to find the best regression model:

library(leaps)

#find best regression model
bestSubsets <- regsubsets(hp ~ mpg + wt + drat + qsec, data=mtcars)

#view results
summary(bestSubsets)

Subset selection object
Call: regsubsets.formula(hp ~ mpg + wt + drat + qsec, data = mtcars)
4 Variables  (and intercept)
     Forced in Forced out
mpg      FALSE      FALSE
wt       FALSE      FALSE
drat     FALSE      FALSE
qsec     FALSE      FALSE
1 subsets of each size up to 4
Selection Algorithm: exhaustive
         mpg wt  drat qsec
1  ( 1 ) "*" " " " "  " " 
2  ( 1 ) " " "*" " "  "*" 
3  ( 1 ) "*" "*" " "  "*" 
4  ( 1 ) "*" "*" "*"  "*" 

The stars ( * ) at the bottom of the output indicate which predictor variables belong in the best regression model for each possible model with a different number of predictor variables.

Here is how to interpret the output:

For a model with only one predictor variable, the best regression model is produced by using mpg as the predictor variable.

For a model with two predictor variables, the best regression model is produced by using wt and qsec as the predictor variables.

For a model with three predictor variables, the best regression model is produced by using mpg, wt and qsec as the predictor variables.

For a model with four predictor variables, the best regression model is produced by using mpg, wt, drat and qsec as the predictor variables.

Note that you can also extract the following metrics for each model:

• rsq :The for each model
• RSS: The for each model
• adjr2: The for each model
• cp: for each model
• bic: The for each model

#view adjusted R-squared value of each model
summary(bestSubsets)$adjr2

[1] 0.5891853 0.7828169 0.7858829 0.7787005

From the output we can see:

• The adjusted R-squared value for the model with mpg as the predictor variable is 0.589.
• The adjusted R-squared value for the model with wt and qsec as the predictor variables is 0.783.
• The adjusted R-squared value for the model with mpg, wt and qsec as the predictor variables is 0.786.
• The adjusted R-squared value for the model with mpg, wt, drat and qsec as the predictor variables is 0.779.

These values give us an idea of how well the set of predictor variables are able to predict the value of the response variable, adjusted for the number of predictor variables in the model.