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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Statistics

NDA 2018 · Mathematics · Statistics

Consider the following statements: 1. If the correlation...

Consider the following statements: 1. If the correlation coefficient rxy=0r_{x y}=0, then the two lines of regression are parallel to each other. 2. If the correlation coefficient rxy=+1\mathrm{r}_{\mathrm{xy}}=+1, then the two lines of regression are perpendicular to each other. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

D. Neither 1 nor 2

Step-by-step solution

We know, \tan \theta=\left|\frac{1-\mathrm{r}_{\mathrm{xy}^2}{\mathrm{r}_{\mathrm{xy}}}\right|\left(\frac{\sigma_{\mathrm{x}} \cdot \sigma_{\mathrm{y}}}{\sigma_{\mathrm{x}^2 \cdot \sigma_{\mathrm{y}^2}\right). If rxy\mathrm{r}_{\mathrm{xy}} is 0 , then tan⁡θ=∞\tan \theta=\infty and lines are perpendicular. If rxy\mathrm{r}_{\mathrm{xy}} is 1 , then the lines are parallel.
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