Allied & ICAR Exam Bank • ALLIED_2750 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Correlation and regression analysis

Question Statement:

If $b_{yx}$ and $b_{xy}$ are the two regression coefficients, the Pearson correlation coefficient $r$ satisfies:

Options:

  • (A) $r = \pm \sqrt{b_{yx} b_{xy}}$
  • (B) $r = b_{yx} + b_{xy}$
  • (C) $r = \frac{b_{yx}}{b_{xy}}$
  • (D) $r = b_{yx} b_{xy}$

Answer Key:

A

Step-by-Step Solution & Explanation

The correlation coefficient is the geometric mean of the two regression coefficients: $r = \pm \sqrt{b_{yx} b_{xy}}$, taking the same sign as the regression coefficients.
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