ACCA Applied Knowledge · Management Accounting · Analytical techniques in budgeting and forecasting
Which statement about the correlation coefficient r and coefficient of determination r² is correct?
If r is 0.6, r squared is 0.36, which is smaller than r. Squaring any value strictly between 0 and 1 in absolute terms reduces it. R squared is never negative and correlation alone does not prove causation.
- AIf r = 0.6 then r² = 0.36, so r² is always smaller than r in absolute value, unless r is 0, 1 or -1Correct
- BIf r = -0.6 then r² = -0.36, showing a negative explained variation
- CA high r² proves that changes in x cause changes in y
- Dr² can take values between -1 and +1
Explanation
Squaring a number between 0 and 1 in absolute value gives a smaller number, so 0.6 gives 0.36; r² equals r only at 0 or 1 (and |r| at -1). r² cannot be negative, so B is wrong. Correlation does not prove causation, so C is wrong, and r² lies between 0 and 1, so D is wrong.
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