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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Statistics

NDA 2017 · Mathematics · Statistics

If two regression lines between height ( x ) and weight ( y ) are 4...

If two regression lines between height ( x ) and weight ( y ) are 4y−15x+410=04 y-15 x+410=0 and 30x−2y−825=030 x-2 y-825=0, then what will be the correlation coefficient between height and weight?

Options

  1. A1/3
  2. B1/2
  3. C2/3
  4. D3/4

Correct answer

B. 1/2

Step-by-step solution

4y−15x+410=0⇒y−154x+4104=0⇒y=154x−4104∴byx=15430x−2y−825=0⇒x=230y+82530∴bxy=230Correlation coeifficient =(byx)(bxy)=154×230=14=12\begin{aligned} & 4 y-15 x+410=0 \\ & \Rightarrow y-\frac{15}{4} x+\frac{410}{4}=0 \Rightarrow y=\frac{15}{4} x-\frac{410}{4} \\ & \therefore b_{y x}=\frac{15}{4} \\ & 30 \mathrm{x}-2 \mathrm{y}-825=0 \Rightarrow \mathrm{x}=\frac{2}{30} \mathrm{y}+\frac{825}{30} \\ & \therefore \mathrm{ b}_{\mathrm{xy}}=\frac{2}{30} \\ & \text{Correlation coeifficient }=\sqrt{\left(\mathrm{b}_{\mathrm{yx}}\right)\left(\mathrm{b}_{\mathrm{xy}}\right)} \\ & =\sqrt{\frac{15}{4} \times \frac{2}{30}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\end{aligned}
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