How to succinctly write a formula with many variables from a data frame?

There is a special identifier that one can use in a formula to mean all the variables, it is the . identifier.

y <- c(1,4,6)
d <- data.frame(y = y, x1 = c(4,-1,3), x2 = c(3,9,8), x3 = c(4,-4,-2))
mod <- lm(y ~ ., data = d)

You can also do things like this, to use all variables but one (in this case x3 is excluded):

mod <- lm(y ~ . - x3, data = d)

Technically, . means all variables not already mentioned in the formula. For example

lm(y ~ x1 * x2 + ., data = d)

where . would only reference x3 as x1 and x2 are already in the formula.

A slightly different approach is to create your formula from a string. In the formula help page you will find the following example :

## Create a formula for a model with a large number of variables:
xnam <- paste("x", 1:25, sep="")
fmla <- as.formula(paste("y ~ ", paste(xnam, collapse= "+")))

Then if you look at the generated formula, you will get :

R> fmla
y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
    x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
    x22 + x23 + x24 + x25