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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Statistics

NDA 2019 · Mathematics · Statistics

For the variables x and y , the two regression lines are 6 x+y=30...

For the variables xx and yy, the two regression lines are 6x+y=306 x+y=30 and 3x+2y=253 x+2 y=25. What are the values of xˉ,yˉ\bar{x}, \bar{y} and rr respectively?

Options

  1. A203,359,−0.5\frac{20}{3}, \frac{35}{9},-0.5
  2. B203,359,0.5\frac{20}{3}, \frac{35}{9}, 0.5
  3. C359,203,−0.5\frac{35}{9}, \frac{20}{3},-0.5
  4. D359,203,0.5\frac{35}{9}, \frac{20}{3}, 0.5

Correct answer

D. 359,203,0.5\frac{35}{9}, \frac{20}{3}, 0.5

Step-by-step solution

Given regression lines 6x+y=30 and 3x+2y=25\begin{aligned} & 6 x+y=30 \\ & \text{ and } 3 x+2 y=25 \end{aligned} point of intersection of both lines =(xˉ,yˉ)=(359,203)for=(\bar{x}, \bar{y})= \left(\frac{35}{9}, \frac{20}{3}\right) for6 x=-y+30\Rightarrow x=-16\frac{1}{6}y+5andforand for2 y=-3 x+25x+25y=−32x+252∴r2=(−16)⋅(−32)⇒r=±12\begin{aligned}& y=-\frac{3}{2}x+\frac{25}{2}\\ & \therefore r²=\left(-\frac{1}{6}\right) \cdot \left(-\frac{3}{2}\right)\\ & \Rightarrow r= \pm \frac{1}{2} \end{aligned}∵\becausesign of xˉ,yˉ&r\bar{x}, \bar{y} \& r is same. ∴r=12\therefore \quad r=\frac{1}{2}
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