Question Bank • QB_EM_161 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Correlation and regression analysis

Question Statement:

In a bivariate data set, the two regression lines are given by $y = 0.4x + 3$ and $x = 0.9y + 2$. Calculate the Karl Pearson correlation coefficient $r$ between $x$ and $y$ (round off to 1 decimal place).

Answer Key:

0.6

Step-by-Step Solution & Explanation

The regression coefficients are $b_{yx} = 0.4$ and $b_{xy} = 0.9$. The correlation coefficient is: $r = \sqrt{b_{yx} \times b_{xy}} = \sqrt{0.4 \times 0.9} = \sqrt{0.36} = 0.6$
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