multiple predictors

Hello,

can anyone provide me with a formula to compute the var of the
residuals in a multiple regression with 3 (uncorrelated) predictors
based on the mean and sd of the predictors, total R^2 and given the
unstandardized regression weights?

For a single predictor this is straightforward (see R syntax below) but
I am obviously doing something wrong when extending it to multiple
predictors - despite the fact that the condition of no
multicollinearity should make it quite easy...

Thank you very much!!!

Manuel


### For a single predictor
b1 <- 3 # fixed reg coefficient
R2 <- 0.6 # squared multiple R
m1 <- 20 # mean predictor
sd1 <- 17 # sd predictor
N <- 1000

x1 <- rnorm(N, m1, sd1)
sdy <- b1/sqrt(R2)*sd1
e <- rnorm(N,0,sdy*sqrt(1-R2))
Y <- b1*x1 + e

a <- lm(Y ~ x1) # check
summary(a)

.

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