Question

If $4\overline{x}-5\overline{y}+33=0$ and $20\overline{x}-9\overline{y}=107$ are two lines of regression, then what are the values of $\overline{x}$ and $\overline{y}$ respectively.

• A. $12$ and $18$
• B. $18$ and $12$
• C. $13$ and $17$
• D. $17$ and $13$

Answer 1

Answer: (C)

$13$ and $17$

The given equations are $4\overline{x}-5\overline{y}+33=0$ .... $\left(i\right)$ and $20\overline{x}-9\overline{y}-107=0$ ..... $\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$, we get

$\overline{x}=13$

Substituting $x$ in $\left(i\right)$, we get

$\overline{y}=17$

Hence, the answer is $13$ and $17$.