Question

If \( \bar{x} = 4 \), \( \bar{y} = 8 \), \( \sigma_x = 2 \), \( \sigma_y = 3 \), and \( r = 0.3 \), then the line of regression of \( y \) on \( x \) is

• A. \( y = 0.45x + 6.2 \)
• B. \( y = 0.55x + 4.2 \)
• C. \( y = 0.45x - 6.2 \)
• D. \( y = 0.55x - 4.2 \)

Hint:

The regression line \( y \) on \( x \) uses the formula \( y - \bar{y} = r \frac{\sigma_y}{\sigma_x}(x - \bar{x}) \).

Answer 1

The Correct Option is A

The regression line of \( y \) on \( x \) is given by: \[ y - \bar{y} = r \frac{\sigma_y}{\sigma_x} (x - \bar{x}) \] Substitute values: \[ y - 8 = 0.3 \cdot \frac{3}{2} (x - 4) = 0.45(x - 4) \Rightarrow y = 0.45x + [8 - 0.45 \cdot 4] = 0.45x + 6.2 \]