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Two quantities x and y have a correlation coefficient of 0.8, the standard deviation of x is 5, and the standard deviation of y is 10. Which of the following is the slope of the least-squares regression line predicting y from x?

  1. A0.4
  2. B0.8
  3. C1.6
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Answer: C. 1.6

The slope of the regression line predicting y from x is the correlation coefficient × (standard deviation of y ÷ standard deviation of x), so 0.8 × 10 ÷ 5 = 1.6. This means that when x increases by 1, the predicted value of y increases by 1.6. The correlation coefficient does not depend on units, but the slope changes with the units and the spreads of x and y.

  • A. This is 0.8 × 5 ÷ 10 = 0.4, with the ratio of the standard deviations inverted.
  • B. This takes the correlation coefficient itself as the slope. The slope equals the correlation coefficient only when the two standard deviations are equal.
  • C. Correct. 0.8 × 10 ÷ 5 = 1.6.
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