Skip to content

FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

Which statement about the relationship between correlation and dependence is correct?

Correlation measures only linear dependence, so two variables can be strongly dependent yet have zero correlation. A classic example is Y equal to X squared with X symmetric around zero, where dependence is perfect but correlation is zero.

  1. AZero correlation implies the variables are independent
  2. BCorrelation captures any nonlinear dependence fully
  3. CCorrelation measures only linear dependence, so dependent variables can have zero correlationCorrect
  4. DCorrelation is unaffected by changes in the joint distribution

Explanation

Pearson correlation measures linear association only. For example, Y = X² with X symmetric about zero has zero correlation with X despite perfect dependence. Zero correlation therefore does not imply independence in general.

Did you get it right without looking?

One question tells you little. A timed set on Empirical Properties of Correlation: How Do Correlations Behave in the Real World? shows your real accuracy, how long you take and where you lose marks.

Practise Empirical Properties of Correlation: How Do Correlations Behave in the Real World?Free diagnostic mock

More Empirical Properties of Correlation: How Do Correlations Behave in the Real World? questions