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I have four features x1,x2,x3,x4. All of their correlation with y are similar in Pearson correlation and in Spearman rank correlation separately. However, all these are +0.15 in Pearson and -0.6 in Spearman, more or less. Does this make sense? How can I interpret this result? All four features and target are definitely related. From a common sense perspective, the sign of Spearman is more accurate as well.

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  • $\begingroup$ The features appear to reflect same trait and are equivalent if you want to model impact or association with y. Further, Spearman correlation is a measure of association(positive or negative). Pearson coefficient generates a coefficient that reflects linearity of the relationship between x feature and y assuming a linear equation for the relationship i.e y = a+ bX. $\endgroup$ Commented Feb 27, 2023 at 13:41
  • $\begingroup$ Have you looked at the plots? (Can you post those plots?) $\endgroup$
    – Dave
    Commented Mar 8, 2023 at 12:41

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Pearson coefficient r shows a low magnitude of correlation. If r-square is close to zero, the relationship is insignificant. Greater the r-square,more is strengthoftherelationship.Pearson method here, fails to identify presence of a significant relationship for a reason e.g. a small sample not yielding Normal Distribution or for other reason.The Spearman measure of (rank) correlation utilizes ranks of two variables to estimate the relationship if any, between feature(s) and target.Here, Spearman correlation value of -0.60 is statistically significant. In the given situation, results of Spearman correlation should be accepted. Moreover,if the sample-size is small,you should avoid using Pearson correlation coefficient.

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  • $\begingroup$ Thank you for the answer. If possible, could you also let me know the significance of the sign in Pearson correlation, if any? $\endgroup$ Commented Mar 8, 2023 at 9:59
  • $\begingroup$ Pearson correlation coefficient simply indicates magnitude of linearity between two variables. r-square shows the magnitude of relationship between two variables. Whether rho = r-square = 0. If it is close to zero, the relationship is insignificant $\endgroup$ Commented Mar 10, 2023 at 23:31

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