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ACCA Applied Knowledge · Management Accounting · Analytical techniques in budgeting and forecasting

Which of the following changes would leave the correlation coefficient between two variables x and y unchanged?

Converting y from dollars to thousands of dollars leaves the correlation coefficient unchanged, because r is unaffected by positive linear rescaling. Multiplying x by -1 would reverse its sign, while outliers or squaring x would alter the linear relationship and so change r.

  1. AMultiplying every x value by -1
  2. BConverting every y value from dollars to thousands of dollarsCorrect
  3. CAdding a single extreme outlier to the data set
  4. DReplacing x with x squared

Explanation

Correlation is unaffected by a positive linear rescaling of either variable, so converting dollars to thousands leaves r unchanged. Multiplying x by -1 reverses the sign of r. An outlier can change r markedly, and squaring x changes the linear relationship.

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