4 ms·

Isn't "Independent and no correlations" redundant? How can two random variables be independent but correlated?

• cjslep 10y ago
  Dependence is stricter than correlation: the population violates probabilistic independence. Correlation can help guide statisticians to finding a dependence between variables, because correlation measures how close or how far a sample is to independence. But this gives rise to the "Correlation does not imply causation" adage. Example of independent but correlated variables: http://www.tylervigen.com/spurious-correlations http://www.tylervigen.com/spurious-correlations
• stan_rogers 10y ago
  An easy example is two thermal sources in the same environment.
• gizmo686 10y ago
  The paper itself does not explicitly require there to be "no correlations". My guess is that that phrase was added by the journalist as emphasis.
• prashnts 10y ago
  Not really. Zero correlation does not necessarily imply independence. From the example on this resource[1]: Let X be a normally distributed random variable with zero mean, and say Y = X^2. Clearly they are not independent. Covariance, which is needed for (pearson) correlation coefficient, can be calculated to be 0: Cov(X, Y) = E(XY) - E(X)E(Y) = E(X^3) - 0 (Since E(X) = mean(X) = 0) = 0 (Since X is centered at 0) [1] http://mathforum.org/library/drmath/view/64808.html http://mathforum.org/library/drmath/view/64808.html