Question

For 10 observations on price (x) and supply (y), the following data was obtained: $\sum x=130,\sum y=220,\sum x^2=2288,\sum y^2=5506$ and $\sum xy=3467$.
What is the line of regression of y on x?

• A. $y=0.91x+8.74$
• B. $y=1.02x+8.74$
• C. $y=1.02x-7.02$
• D. $y=0.91x-7.02$

Answer 1

Answer: (B)

$y=1.02x+8.74$

Line of regression of $y$ on $x$ is : $y-\overline{y}=b_{yx}(x-\overline{x})$ where $\overline{y}$ and $\overline{x}$ are mean values.

$\therefore \overline{y}=22,\overline{x}=13$ as $n=10$

Also, $b_{yx}=r\frac{{\sigma }_y}{{\sigma }_x}$

$\therefore r=\frac{n\sum -(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x{)}^2\left]\right[n\sum y^2-(\sum y{)}^2]}}=0.962$

${\sigma }_y=8.2$ and ${\sigma }_x=7.73$

$\therefore b_{yx}=1.02$

$\therefore y=1.02x+8.74$ is the required line of regression.