Discussion
When the correlation coefficient r = 0, then the two regression lines are :
Answer: A
When r = 0 the regression lines are perpendicular to each other.
The two regression lines are
\[ \begin{aligned} y - \bar{y} &= r\frac{\sigma_{y}}{\sigma_{x}}(x - \bar{x}) \\ x - \bar{x} &= r\frac{\sigma_{x}}{\sigma_{y}}(y - \bar{y}) \end{aligned} \]
With r = 0 the first becomes \(y = \bar{y}\), a horizontal line, and the second becomes \(x = \bar{x}\), a vertical line, so they cross at right angles at the point of means.
The lines coincide only when r = +1 or -1, perfect correlation. They are never parallel, because both always pass through \((\bar{x}, \bar{y})\), and they exist for any data with non-zero variances.
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