No. Pearson correlation coefficient between 2 variables might be zero even when they have a relationship between them. Example: x and x^2
Card 1 of 259. Answer: No. Pearson correlation coefficient between 2 variables might be zero even when they have a relationship between them. Example: x and x^2
About · Quizzes · History of AI · To suggest new questions or report an error send me a dm.
No. A Pearson correlation of 0 only means there is no linear relationship between the two variables. They can still be strongly, even perfectly, related in a non-linear way.
The classic example is y = x² with x spread symmetrically around zero, say from −3 to 3. y is completely determined by x, yet the correlation is 0, because the rising half of the curve cancels the falling half. A circle, a U-shape or a sine wave over a full period can all produce correlations near zero.
Always plot the data before trusting the coefficient, as Anscombe's quartet famously shows. To detect monotonic relationships use Spearman's rank correlation, and for general dependence use mutual information or distance correlation, which is zero only when the variables are truly independent. The reverse direction does hold: independent variables always have zero correlation.
