Correlation Coefficients and it's implications

[Matheus-Emanue123]

📊 Let's Talk About Correlation Coefficients!

Hi everyone! 👋

As part of the StellarInsights project, I explored different correlation coefficients to analyze the relationship between stellar features (like stmass) and planetary characteristics (pldens, for instance).

Some of the correlation measures used:

• Pearson Correlation – to capture linear relationships
• Spearman Correlation – for monotonic (non-linear) associations
• Kendall's Tau – useful for smaller datasets or ties
• Distance Correlation – detects non-linear dependencies
• Mutual Information – from information theory, very flexible

💡 Interesting finding: Even the non-linear measures revealed weak associations between stellar mass and planetary density within Earth-like clusters. This may suggest that other factors (e.g., planetary composition or system architecture) play a more important role.

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🤔 A few questions for the community:

1. Which of these correlation metrics do you typically use in your research or data analysis?
2. Has anyone here applied mutual information or distance correlation in a different scientific context (e.g., biology, social networks)?
3. Do you think it's worth including more stellar parameters like age, activity level, or disk properties?
4. Any ideas on how to better capture complex non-linear relationships?

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Looking forward to hearing your thoughts and exchanging ideas! 😄
Best,
@Matheus-Emanue123