correlated random variables

correlatedrandomvariables.r

## make it reproducible

set.seed(8675309)


## two normally distributed variables

X1 <- rnorm(100, mean = 0, sd = 1) 
X2 <- rnorm(100, mean = 0, sd = 1) 

plot(X1, X2)


# set approximate R-square value
Rsq <- 0.90

# create Y and Z
Y <- X1 
Z <- Rsq * X1 + sqrt(1 - Rsq) * X2 

# evaluate
cor(Y,Z)

plot(Y, Z)


### -----------------------------------------------------------------------------------------

## a binomial variable between 1 and 10 and a normally distributed variable

set.seed(8675309)

X1 <- rbinom(100, 10, 0.5) 
X2 <- rnorm(100, mean = 0, sd = 1) 

plot(X1, X2)


# set approximate R-square value
Rsq <- 0.90

# create Y and Z
Y <- X1 
Z <- Rsq * X1 + sqrt(1 - Rsq) * X2 

# evaluate
cor(Y,Z)

plot(Y, Z)


### -----------------------------------------------------------------------------------------

## two uniform variables between 1 and 10

set.seed(8675309)

X1 <- sample(1:10, 100, replace = TRUE) 
X2 <- sample(1:10, 100, replace = TRUE)  

plot(X1, X2)


# set approximate R-square value
Rsq <- 0.80

# create Y and Z
Y <- X1 
Z <- Rsq * X1 + sqrt(1 - Rsq) * X2

Z <- floor(Z)

# evaluate
cor(Y,Z)

plot(Y, Z)