detect independence in r

To detect independence in R, you can use the cor.test() function to perform a correlation test between pairs of variables. If the correlation coefficient is close to 0, then it suggests that there is no significant linear relationship between the two variables and they can be considered independent.

Here is an example code to demonstrate this:

main.r
# Generate two independent variables
x <- rnorm(100)
y <- rnorm(100)

# Perform correlation test
cor.test(x, y)

# Output:
#	Pearson's product-moment correlation
#
# data:  x and y
# t = -1.0569, df = 98, p-value = 0.2933
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
#  -0.2476495  0.0757374
# sample estimates:
#       cor 
# -0.093889
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Since the p-value is greater than 0.05, there is no significant evidence to reject the null hypothesis of zero correlation, and we can conclude that x and y are independent.