Is it possible to fit a linear model with only a response variable?

Question

If I do this, I get two coefficients (intercept and year)

data <- data.frame(accidents=c(3,1,5,0,2,3,4), year=1:7)
glm(accidents ~ year, family=poisson(link = log), data)

Coefficients:
(Intercept)         year  
     0.7155       0.0557

But the correct answer is 0.944

data <-data.frame(accidents=c(3,1,5,0,2,3,4))
glm(accidents ~ ., family=poisson(link=log), data)

Coefficients:
(Intercept)  
  0.944 

Is there a way to specify the glm formula for just the response variable? If I use the second formula with the first data frame I get the wrong answer because the "." also includes the "year". In the second data frame I'm cheating because there is only one column.

Answer 1

Here's the incantation that you are looking for:

glm(accidents ~ 1, family=poisson(link = log), data)

Using it with your original data frame:

data <- data.frame(accidents=c(3,1,5,0,2,3,4), year=1:7)
coef(glm(accidents ~ 1, family=poisson(link = log), data))
(Intercept) 
  0.9444616 

Also, as Ben Bolker mentions, the R Introduction document that ships with R includes a nicely informative section on the grammar of the formula interface.