Question Bank • QB_EM_ADV_076 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Correlation and regression analysis

Question Statement:

If the two linear regression coefficients between variables $X$ and $Y$ are $b_{yx} = 0.8$ and $b_{xy} = 0.45$, then the Karl Pearson correlation coefficient $r$ is:

Options:

  • (A) $0.60$
  • (B) $0.36$
  • (C) $0.72$
  • (D) $0.50$

Answer Key:

A

Step-by-Step Solution & Explanation

The correlation coefficient $r$ is the geometric mean of the two regression coefficients with the same sign as the coefficients: $r = \pm \sqrt{b_{yx} \cdot b_{xy}}$ Since both $b_{yx} = 0.8 > 0$ and $b_{xy} = 0.45 > 0$ are positive: $r = +\sqrt{0.8 \times 0.45} = \sqrt{0.36} = 0.60$
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