Allied & ICAR Exam Bank • ALLIED_2756 MSQ • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Correlation and regression analysis

Question Statement:

Which of the following statements are TRUE for the regression coefficients $b_{yx}$ and $b_{xy}$?

Options:

  • (A) Both $b_{yx}$ and $b_{xy}$ must always have the same algebraic sign
  • (B) Their product $b_{yx} b_{xy}$ cannot exceed $1$
  • (C) If one regression coefficient exceeds $1$, the other must be less than $1$
  • (D) The arithmetic mean of $b_{yx}$ and $b_{xy}$ is always greater than or equal to $|r|$

Answer Key:

A, B, C, D

Step-by-Step Solution & Explanation

Since $r^2 = b_{yx} b_{xy} \le 1$, they share signs, their product is $\le 1$, if one exceeds 1 the other must be
lt; 1$, and AM $\ge$ GM implies $\frac{b_{yx} + b_{xy}}{2} \ge \sqrt{b_{yx} b_{xy}} = |r|$.
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