[R] Combining two models into one

[luana]

Hi guys,
I'm trying to combining 2 models into 1 but maybe I'm not doing this in the
right way.
my dataset is about the level of the vitamin A in the blood measured at
different times with two different treatments (ie. I have 6 coloums, vit A1
, time1, treat1, vit A2, time2, treat2, n=28). It wants to determinate if
the variable treatment is really appropriate.
E(y) = β0 + β1 x +  β2 x^2 (treatment1)
      =  γ0 +  γ1 x +  γ2 x^2 (treatment2)
(level of vit a against time)

satisfy the hypothesis H0 :  β1 = γ1 and β2 =  γ2 .

The question is how can I combine the two models into one E(y) = X β with
appropriate design matrix X and coefficient vector β? In this question β  is
6x1.

I did it but I think it is not good at all:

vita<-cbind(dt$Vita..y., dt$Time..x.,
dt$Treatment,dt$Vita..y..1,dt$Time..x..1,dt$Treatment.1)


x1 <- cbind(rep(1,28), matrix(0,28,2), vita[,1], matrix(0,28,2))
x11 <- cbind(rep(1,28), matrix(0,28,2), vita[,4], matrix(0,28,2))
x2 <- cbind(rep(0,28), rep(1,28), matrix(0,28,2), vita[,2], rep(0,28))
x22 <- cbind(rep(0,28), rep(1,28), matrix(0,28,2), vita[,5], rep(0,28))
x3 <- cbind(matrix(0,28,2), rep(1,28), matrix(0,28,2), vita[,3])
x33 <- cbind(matrix(0,28,2), rep(1,28), matrix(0,28,2), vita[,6])

x <- rbind(x1, x2, x3,x11, x22, x33) #create the design matrix

ma <-c(vita[,1],vita[,4])  #response values

mma <- data.frame(ma,x) #create the data frame for regression

attach(mma) #attach the data frame to make it available to lm()

ma.lm <- lm(ma ~ -1 + X1 + X2 + X3 + X4 + X5 + X6) #regr model without
#intercept (note the -1 term)

I am sure that is not good, because I should have x^2  and there isn't.
Moreover it gives me an error:
Error in model.frame.default(formula = ma ~ -1 + X1 + X2 + X3 + X4 + X5 +  : 
  variable lengths differ (found for 'X1')

How can I do it?

Tnx



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