Question

For the variables $x$ and $y$, the regression equations are given as $7x-3y-18=0$ and $4x-y-11=0$. Identify the regression equation of $y$ on $x$.

• A. $4x-y-11=0$
• B. $7x-3y-18=0$
• C. $4x-y-2=0$
• D. $7x-3y-4=0$

Answer 1

The correct option is B $7x-3y-18=0$

Let us assume that $7x-3y-18=0$ is the regression equation of $y$ on $x$.

Consider $7x-3y-18=0$

$\Rightarrow y=-6+\frac{7}{3}x$

$\therefore b_{yx}=\frac{7}{3}$

Now consider $4x-y-11=0$

$\Rightarrow x=\frac{11}{4}+\frac{1}{4}y$

$\therefore b_{xy}=\frac{1}{4}$

Now taking the product, $b_{yx}\times b_{xy}=\frac{7}{3}\times \frac{1}{4}=\frac{7}{12}<1$

Since the product is less than one, our assumptions are correct.

Thus $7x-3y-18=0$ is the regression equation of $y$ on $x$.