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As mentioned above, I have a problem where I need to generate new data Y from an existing data X such that Y is p correlated to X.

I know their are several ways to do it but I want to know if monte Carlo simulation could be used to achieve this goal. If it is possible, could you point me in the right direction so that I can learn more about it and implement it too?

Example: data is X = [2, 4, 9, 10]

Generate new Y such that it has 4 values and it is p=0.75 percent correlate to X.

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  • $\begingroup$ Correlation is not a percentage - it goes from -1 to 1. The square of correlation can be construed as a percentage $\endgroup$
    – Glen_b
    Commented Oct 24, 2021 at 5:09
  • $\begingroup$ Yup that's my mistake, let me change it to say it's 0.75 correlated $\endgroup$
    – Rishabh Agrawal
    Commented Oct 24, 2021 at 5:10
  • $\begingroup$ It still says 'percent' at the end of the question. $\endgroup$
    – Glen_b
    Commented Oct 24, 2021 at 5:23
  • $\begingroup$ I think considering a linear model $Y = \alpha X + \varepsilon$, where $\varepsilon \sim \mathcal{N}(0, 1)$ are i.i.d. could be a good way to do so. Now you just need to find the adequate value of $\alpha$ using what you know on correlation... $\endgroup$
    – Pohoua
    Commented Oct 24, 2021 at 10:50

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