different possible combinations of variables for a generalized linear model

Question

Is there a method in R to run a GLM for each of the different variables in a data frame with a different combinations e.g.

If I have 4 explanatory variables I can mo

Answer 1

This is called dredging:

library(MuMIn)
data(Cement)
fm1 <- lm(y ~ ., data = Cement)
dd <- dredge(fm1)

Global model call: lm(formula = y ~ ., data = Cement)
---
Model selection table 
   (Intrc)    X1      X2      X3      X4 df  logLik  AICc delta weight
4    52.58 1.468  0.6623                  4 -28.156  69.3  0.00  0.566
12   71.65 1.452  0.4161         -0.2365  5 -26.933  72.4  3.13  0.119
8    48.19 1.696  0.6569  0.2500          5 -26.952  72.5  3.16  0.116
10  103.10 1.440                 -0.6140  4 -29.817  72.6  3.32  0.107
14  111.70 1.052         -0.4100 -0.6428  5 -27.310  73.2  3.88  0.081
15  203.60       -0.9234 -1.4480 -1.5570  5 -29.734  78.0  8.73  0.007
16   62.41 1.551  0.5102  0.1019 -0.1441  6 -26.918  79.8 10.52  0.003
13  131.30               -1.2000 -0.7246  4 -35.372  83.7 14.43  0.000
7    72.07        0.7313 -1.0080          4 -40.965  94.9 25.62  0.000
9   117.60                       -0.7382  3 -45.872 100.4 31.10  0.000
3    57.42        0.7891                  3 -46.035 100.7 31.42  0.000
11   94.16        0.3109         -0.4569  4 -45.761 104.5 35.21  0.000
2    81.48 1.869                          3 -48.206 105.1 35.77  0.000
6    72.35 2.312          0.4945          4 -48.005 109.0 39.70  0.000
5   110.20               -1.2560          3 -50.980 110.6 41.31  0.000
1    95.42                                2 -53.168 111.5 42.22  0.000