Question

Given $$ x = 4y + 5, \quad y = Kx + 4, $$ the lines of regression of $ x $ on $ y $ and $ y $ on $ x $ respectively. What is the value of $ K $, if the value of correlation coefficient $ r = 0.5 $?

• A. \( \frac{1}{8} \)
• B. \( \frac{1}{17} \)
• C. \( \frac{1}{16} \)
• D. \( \frac{1}{15} \)

Hint:

Correlation squared equals product of regression coefficients.

Answer 1

The Correct Option is C

Using regression and correlation relations: \[ r^2 = m_1 m_2 \] Where \( m_1 = 4 \), \( m_2 = K \), and \( r = 0.5 \): \[ 0.5^2 = 4 \times K \implies 0.25 = 4 K \implies K = \frac{1}{16} \]