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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Statistics

NDA 2017 · Mathematics · Statistics

It is given that X =10, Y =90, σ_X=3, σ_Y=12 and r_ XY =0.8 . The...

It is given that Xˉ=10,Yˉ=90,σX=3,σY=12\bar{X}=10, \bar{Y}=90, \sigma_X=3, \sigma_Y=12 and rXY=0.8\mathrm{r}_{\mathrm{XY}}=0.8. The regression equation of XX on YY is

Options

  1. AY=3.2X+58\mathrm{Y}=3.2 \mathrm{X}+58
  2. BX=3.2Y+58\mathrm{X}=3.2 \mathrm{Y}+58
  3. CX=−8+0.2Y\mathrm{X}=-8+0.2 \mathrm{Y}
  4. DY=−8+0.2X\mathrm{Y}=-8+0.2 \mathrm{X}

Correct answer

C. X=−8+0.2Y\mathrm{X}=-8+0.2 \mathrm{Y}

Step-by-step solution

X‾=10,Y‾=90,σx=3,σy=12,rxy=0.8\overline{\mathrm{X}}=10, \overline{\mathrm{Y}}=90, \sigma_{\mathrm{x}}=3, \sigma_{\mathrm{y}}=12, \mathrm{r}_{\mathrm{xy}}=0.8 Regression equation x on y is x−10=r⋅σxσy(y−90)x-10=r \cdot \frac{\sigma_x}{\sigma_y}(y-90)⇒x−10=0.8×312(y−90)⇒x−10=2.412(y−90)\begin{aligned} & \Rightarrow \mathrm{x}-10=0.8 \times \frac{3}{12}(\mathrm{y}-90) \\ & \Rightarrow \mathrm{x}-10=\frac{2.4}{12}(\mathrm{y}-90)\end{aligned}$\begin{aligned} & \Rightarrow x-10=0.2(y-90) \\ & \Rightarrow x-10=0.2 y-18 \\ & \Rightarrow x=0.2 y-8.\end{aligned}
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