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CA Foundation · Quantitative Aptitude · Correlation and Regression

For variables x and y, the regression coefficient of y on x is 0.8. New variables are defined as u = x/5 + 7 and v = y/2 – 3. What is the regression coefficient of v on u?

The regression coefficient of v on u is 2.0. Shifts of origin (+7, –3) have no effect, but scaling matters. The coefficient is multiplied by the ratio of the scale factor of v to that of u, which is 0.8 × (1/2)/(1/5) = 2.0.

  1. A0.8
  2. B0.32
  3. C2.0Correct
  4. D4.0

Explanation

Regression coefficients are independent of a change of origin but depend on scale. Here u = x/5 + 7 and v = y/2 – 3. So bvu = byx × (1/2)/(1/5) = 0.8 × 2.5 = 2.0. The value 0.8 ignores the scale change, and 0.32 inverts the ratio of scale factors.

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