In [1]:
n1 <- 100
xm1 <- 10
ym1 <- 20
sx1 <- 5
sy1 <- 8
r1 <- 0.7
In [2]:
n2 <- 200
xm2 <- 12
ym2 <- 22
sx2 <- 6
sy2 <- 10
r2 <- 0.8
In [3]:
n <- n1 + n2
In [4]:
sum_xy1 <- n1 * (r1 * sx1 * sy1 + xm1 * ym1)
sum_xy2 <- n2 * (r2 * sx2 * sy2 + xm2 * ym2)
sum_xy <- sum_xy1 + sum_xy2
In [5]:
xm <- (n1 * xm1 + n2 * xm2) / n
ym <- (n1 * ym1 + n2 * ym2) / n
cov_xy <- 1/n * sum_xy - xm * ym
In [6]:
sxn_sq <- 1/n * ((sx1^2+xm1^2) * n1 + (sx2^2+xm2^2) * n2) - xm^2
syn_sq <- 1/n * ((sy1^2+ym1^2) * n1 + (sy2^2+ym2^2) * n2) - ym^2
In [7]:
r <- cov_xy / sqrt(sxn_sq * syn_sq)
r
Out[7]: