NDA 2016
- Exam
- NDA
- Year
- 2016
- Subject
- Mathematics
- Chapter
- Statistics
NDA 2016 · Mathematics · Statistics
For 10 observations on price ( x ) and supply (y), the following...
For 10 observations on price ( ) and supply (y), the following data was obtained:
What is line of regression of y on x ?
Options
- A
- B
- C
- D
Correct answer
B.
Step-by-step solution
Line of regression of on is :
\begin{aligned}
& \begin{aligned}
& y-\bar{y}=b_{y x}(x-\bar{x}) \\
& \bar{y}=\frac{\Sigma y}{n} ; \bar{x}=\frac{\Sigma x}{n} \Rightarrow \bar{y}=\frac{220}{10}=22 ; \bar{x}=\frac{130}{10}=13 \\
& b_{y x}=\mathrm{r} \cdot \frac{\sigma_y}{\sigma_x} \\
& \mathrm{r}=\frac{n \Sigma x y-(\Sigma x)(\Sigma y)}{\sqrt{\left[n \Sigma x^2-(\Sigma x)^2\right]\left[n \Sigma y^2-(\Sigma y)^2\right]}} \\
&=\frac{10(3467)-(130)(220)}{\sqrt{\left[(10 \times 2288)-130^2\right]\left[(10 \times 5506)-\left(220^2\right)\right]}} \\
& \mathrm{r}=0.962 \\
& \sigma_y=\sqrt{\frac{\Sigma y^2}{n}-\left(\frac{\Sigma y}{n}\right)^2} \Rightarrow \sigma_y=8.2 ; \sigma_x=7.73 . \\
& \Rightarrow b_{x y}=0.962 \times \frac{8.2}{7.73}=1.02
\end{aligned}
\end{aligned}\Rightarrowyx\begin{gathered}
y-22=1.02(x-13) \\
\Rightarrow y=1.02 x+8.74
\end{gathered}$