Let two lines of regression be \( x + y + 11 = 0 \) and \( 2x + 3y + 4 = 0 \) for some data. What is the value of correlation coefficient between x and y ?
- A. -\sqrt{\frac{2}{3}} ✓
- B. -\sqrt{\frac{1}{6}}
- C. \sqrt{\frac{2}{3}}
- D. \sqrt{\frac{1}{6}}
Correct Answer: A. -\sqrt{\frac{2}{3}}
Explanation
Assuming y on x is 2x+3y+4=0, we get b_yx = -2/3. Assuming x on y is x+y+11=0, we get b_xy = -1. Then r^2 = (-2/3)(-1) = 2/3. Since both regression coefficients are negative, r must be negative, so r = -\sqrt{2/3}.
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