Question

If the angle between the two lines of regression is$90°$, then it represents

• A. Perfect correlation
• B. Perfect negative correlation
• C. No linear correlation
• D. None of the above

Answer 1

The correct option is C

No linear correlation

Explanation for Correct Option:

Step 1: The angle between the line of regression is $\theta ,$ then

$\therefore \tan \theta =\left\{\frac{[1–r^2]}{r}\right\}\times \left\{\frac{[x.y]}{[x^2+y^2]}\right\}...........\left(\mathrm{i}\right)$

Since $\theta =90°,r=0$

Step 2: Putting the value of $\theta$ and in equation (i)

$\tan 90°=\left\{\frac{[1–0]}{0}\right\}\times \left\{\frac{[x.y]}{[x^2+y^2]}\right\}$

Since $\tan 90°=\infty$

Therefore, there is no linear correlation.

Hence option (3) is correct.