multivariate regression

I have two dependents that both depent on two variables AND on each other, can this be modelled in R (must be!) but I can't figure out how, anyone a hint?

In clear terms:

I want to model my data with the following model:

Y1=X1*coef1+X2*coef2
Y2=X1*coef2+X2*coef3

Note: 开发者_如何学Ccoef2 appears in both lines Xi, Yi is input and output data respectively

I got this far:

lm(Y1~X1+X2,mydata)

now how do I add the second line of the model including the cross dependency?

Your help is greatly appreciated! Cheers, Bastiaan

---

Try this:

# sample data - true coefs are 2, 3, 4
set.seed(123)
n <- 35
DF <- data.frame(X1 = 1, X2 = 1:n, X3 = (1:n)^2)
DF <- transform(DF, Y1 = X1 * 2 + X2 * 3 + rnorm(n), 
          Y2 = X1 * 3 + X2 * 4 + rnorm(n))

# construct data frame for required model
DF2 <- with(DF, data.frame(y = c(Y1, Y2), 
x1 = c(X1, 0*X1),
x2 = c(X2, X1),
x3 = c(0*X2, X2)))

lm(y ~. - 1, DF2)

We see it does, indeed, recover the true coefs of 2, 3, 4:

> lm(y ~. - 1, DF2)

Call:
lm(formula = y ~ . - 1, data = DF2)

Coefficients:
   x1     x2     x3  
2.084  2.997  4.007