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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Statistics

NDA 2020 · Mathematics · Statistics

Let X and Y represent prices (in ₹) of a commodity in Kolkata and...

Let XX and YY represent prices (in ₹) of a commodity in Kolkata and Mumbai respectively. It is given that X=65,Y=67X=65, Y=67, σX=2.5,σY=3.5\sigma_X=2.5, \sigma_Y=3.5 and r(X,Y)=0.8r(X, Y)=0.8. What is the equation of regression of YY on XX ?

Options

  1. AY=0.175X−5Y=0.175 X-5
  2. BY=1.12X−5.8Y=1.12 X-5.8
  3. CY=1.12X−5Y=1.12 X-5
  4. DY=0.17X+5.8Y=0.17 X+5.8

Correct answer

B. Y=1.12X−5.8Y=1.12 X-5.8

Step-by-step solution

Regression of YY on X:X :Y={σyσx×r(x,y)}X−a( where a= constant term )⇒Y=(3.52.5×0.8)X−5.8∴Y=1.12X−5.8\begin{aligned} & Y=\left\{\frac{\sigma_y}{\sigma_x} \times r(x, y)\right\} X-a(\text{ where } a=\text{ constant term }) \\ & \Rightarrow Y=\left(\frac{3.5}{2.5} \times 0.8\right) X-5.8 \\ & \therefore Y=1.12 X-5.8 \end{aligned}$$
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