In my opinion is a mixed linear model a better approach for this kind of data. The code below given in the fixed effect the overall trend. The random effects indicate how the trend for each individual state differ from the global trend. The correlation structure takes the temporal autocorrelation into account. Have a look at Pinheiro & Bates (Mixed Effects Models in S and S-Plus).
library(nlme)
lme(response ~ year, random = ~year|state, correlation = corAR1(~year))
## make fake data
library(data.table)
set.seed(1)
dat <- data.table(x=runif(100), y=runif(100), grp=rep(1:2,50))
##calculate the regression coefficient r^2
dat[,summary(lm(y~x))$r.squared,by=grp]
grp V1
1: 1 0.01465726
2: 2 0.02256595
as well as all the other output from summary(lm):
dat[,list(r2=summary(lm(y~x))$r.squared , f=summary(lm(y~x))$fstatistic[1] ),by=grp]
grp r2 f
1: 1 0.01465726 0.714014
2: 2 0.02256595 1.108173
library(lme4)
d <- data.frame(state=rep(c('NY', 'CA'), c(10, 10)),
year=rep(1:10, 2),
response=c(rnorm(10), rnorm(10)))
xyplot(response ~ year, groups=state, data=d, type='l')
fits <- lmList(response ~ year | state, data=d)
fits
#------------
Call: lmList(formula = response ~ year | state, data = d)
Coefficients:
(Intercept) year
CA -1.34420990 0.17139963
NY 0.00196176 -0.01852429
Degrees of freedom: 20 total; 16 residual
Residual standard error: 0.8201316
Here's an approach using the plyr package:
d <- data.frame(
state = rep(c('NY', 'CA'), 10),
year = rep(1:10, 2),
response= rnorm(20)
)
library(plyr)
# Break up d by state, then fit the specified model to each piece and
# return a list
models <- dlply(d, "state", function(df)
lm(response ~ year, data = df))
# Apply coef to each model and return a data frame
ldply(models, coef)
# Print the summary of each model
l_ply(models, summary, .print = TRUE)
The lm() function above is an simple example. By the way, I imagine that your database has the columns as in the following form:
year state var1 var2 y...
In my point of view, you can to use the following code:
require(base)
library(base)
attach(data) # data = your data base
#state is your label for the states column
modell<-by(data, data$state, function(data) lm(y~I(1/var1)+I(1/var2)))
summary(modell)