How to simulate a strong correlation of data with R-CodePudding

Sometimes I try to simulate data by using the rnorm function, which I have done below:

mom.iq <- rnorm(n=1000,
                mean=120,
                sd=15)
kid.score <- rnorm(n=1000,
                   mean=45,
                   sd=20)
df <- data.frame(mom.iq,
                 kid.score)

But when I plot something like this, it usually ends up with data thats highly uncorrelated:

library(ggpubr)

ggscatter(df,
          x="mom.iq",
          y="kid.score") 
  geom_smooth(method = "lm")

However, I would like to simulate something with a stronger correlation if possible. Is there an easy way to do this within R? I'm aware that I could just as easily just produce my own values manually, but thats not super practical for recreating large samples.

CodePudding user response：

What you are doing is to generate two independent variables; so, it is normal not to be correlated. What you can do is this:

# In order to make the values reproducible
  set.seed(12345)

# Generate independent variable
  x <- rnorm(n=1000, mean=120, sd=15)
# Generate the dependen variable
  y <- 3*x   6   rnorm(n=1000, mean = 0, sd = 5)

I used 3 and 6, but you can define them as you want (a and b) in order to get a linear dependence defined as y = a*x b.

The sum of rnorm(n=1000, mean = 0, sd = 5) is done to add some variability and avoid a perfect correlation between x and y. If you want to get a more correlated data, reduce the standard deviation (sd) and to get a lower correlation, increase its value.

CodePudding user response：

You can create your second variable by taking the first variable into account, and adding some error with rnorm in order to avoid making the relationship completely deterministic/

library(ggplot2)

dat <- data.frame(father_age = rnorm(1000, 35, 5)) |> 
  dplyr::mutate(child_score = -father_age * 0.5   rnorm(1000, 0, 4))

dat |> 
  ggplot(aes(father_age, child_score))  
  geom_point()  
  geom_smooth(method = "lm")
#> `geom_smooth()` using formula 'y ~ x'

^{Created on 2022-07-07 by the}