Constrained linear regression coefficients in R [duplicate]

Answer 1

If the x and y values are the same, then you could use this model:

lm( I(z1+z2)~ x +y )  # Need to divide coefficients by 2

If they are separate data then you could rbind the two datasets after renaming z2 to z1.

Answer 2

For your specified regression:

Px = ax*Qx + bxy*Qy + cy
Py = ay*Qy + bxy*Qy + cy

We can introduce a grouping factor:

id <- factor(rep.int(c("Px", "Py"), c(length(Px), length(Py))),
             levels = c("Px", "Py"))

We also need to combine data:

z <- c(Px, Py)    ## response
x <- c(Qx, Qy)    ## covariate 1
y <- c(Qy, Qy)    ## covariate 2    

Then we can fit a linear model using lm with a formula:

z ~ x + y + x:id