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A correlation of or around zero can be interpreted as which of the following ?

  • A.A curvilinear relationship is present
  • B.A linear relationship is present
  • C.It could mean either no relationship or curvilinear one
  • D.No relationship is present

Answer: C

A correlation near zero could mean either no relationship or curvilinear one.

The Pearson correlation coefficient measures only the strength of a linear relationship. A value near zero says there is no straight-line relationship, but the variables may still be strongly related in a curve. Arousal and performance, for example, follow an inverted U, which can give a correlation close to zero.

So it is wrong to conclude that no relationship exists, or that the relationship must be curvilinear, and a linear relationship is exactly what a zero correlation rules out. A scatter plot shows which case applies.

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