Question

For the variables $x$ and $y$, the regression equations are given as $7x-3y-18=0$ and $4x-y-11=0$. Find the arithmetic means of $x$ and $y$ respectively.

• A. $3$ and $1$
• B. $1$ and $3$
• C. $2$ and $4$
• D. $4$ and $2$

Answer 1

The correct option is A $3$ and $1$

Since the two lines of regression interest at the point $(\overline{X},\overline{Y})$

Replace $x$ and $y$ by $\overline{X}$ and $\overline{Y}$ respectively in the given regression equations.

We get,

$7\overline{X}-3\overline{Y}-18=0$ and $4\overline{X}-\overline{Y}-11=0$

Solving these equations, we get $\overline{X}=3$ and $\overline{Y}=1$

Thus the arithmetic mean of $x$ and $y$ is given by $3$ and $1$ respectively.