Question
Does zero correlation mean independence?
✓
Answer
No, Zero correlation does not mean absence of correlation but it means absence of linear correlation. There may be a non linear relationship between two variables but variables which have non linear relationship will depict zero correlation when put to scatter diagram and low correlation when used Pearson's or Spearman's method. Consider a shape as shown below:
It will be taken as zero correlation but to a certain level, X and Y are positively related and thereafter their relationship becomes negative.
It will be taken as zero correlation but to a certain level, X and Y are positively related and thereafter their relationship becomes negative.
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