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CA Foundation · Quantitative Aptitude · Correlation and Regression

Let u = (x - 10)/5 and v = (30 - y)/2. For the data, r(u, v) = 0.6, σu = 2 and σv = 3. What is the regression coefficient of y on x (b_yx)?

The regression coefficient of y on x is -0.36. Scales give σx = 10 and σy = 6, and the opposite direction of v relative to y makes r(x, y) = -0.6. Then b_yx = -0.6 × 6/10 = -0.36.

  1. A-0.36Correct
  2. B0.36
  3. C-0.60
  4. D-1.00

Explanation

σx = 5 × 2 = 10 and σy = 2 × 3 = 6. Since u increases with x but v decreases as y increases, r(x, y) = -0.6. Then b_yx = r × σy/σx = -0.6 × 6/10 = -0.36. Option -1.00 is b_xy (σx/σy used), and 0.36 ignores the sign reversal.

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