summary many regressions

Dear R users,

I have a large data set which includes data from 300 cities. I want to run
a biviriate regression for each city and record the coefficient and the
adjusted R square.

For example, in the following, I have 10 cities represented by numbers from
1 to 10:

x = cumsum(c(0, runif(999, -1, +1)))
y = cumsum(c(0, runif(999, -1, +1)))
city = rep(1:10,each=100)
data<-data.frame(cbind(x,y,city))

I can manually run regressions for each city:
fit_city1 <- lm(y ~ x,data=subset(data,data$city==1))
summary(fit_city1)

Obvious, it is very tedious to run 300 regressions. I wonder if there is a
quicker way to do this. Use for loop?  what I want to see is something like
this:

City        Coefficient       Adjusted R square
1              -0.05                  0.36
2              -0.12                  0.20
3              -0.05                  0.32
.....

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