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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Statistics

NDA 2015 · Mathematics · Statistics

The regression coefficients of a bivariate distribution are -0.64...

The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

Options

  1. A0.48
  2. B-0.48
  3. C0.50
  4. D-0.50

Correct answer

B. -0.48

Step-by-step solution

Let b1=−0.64b_1=-0.64b2=−0.36r=±−0.64×−0.36=±0.48∵b1<0b2<0∴r<0⇒r=−0.48\begin{aligned} & \mathrm{b}_2=-0.36 \\ & \mathrm{r}= \pm \sqrt{-0.64 \times-0.36}= \pm 0.48 \\ & \because \mathrm{ b}_1 < 0 & \mathrm{ b}_2 < 0 \\ & \therefore \mathrm{r} < 0 \\ & \Rightarrow \mathrm{r}=-0.48 \end{aligned}$$
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