I can see your confusion. To understand why I said that variables that have “zero correlation” might still be related, you need to remember that we were speaking of traditional correlation which is a linear relationship. We were discussing the Pearson moment correlation which we designate as “r.” An r of zero tells us that the two variables in question are not linearly related. Variables that have no linear relationship might still be related in non-linear ways. For example, two variables with an r of zero might have a “curvilinear” relationship as in this graph:

Zero Correlation with Curvilinear relationship
Zero Correlation with Curvilinear Relationship

We are not going to get into this topic in this course, but we could develop an equation of a curve that ‘best fits’ this data distribution. Thus these two variables have a zero linear relationship but a strong curvilinear relationship.

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