Question

Find the line of regression of y on x from the following table.

x	$1$	$2$	$3$	$4$	$5$
y	$7$	$6$	$5$	$4$	$3$

Hence, estimate the value of y when $x=6$.

Answer 1

Regression is of $y$ on $x$:

$\therefore y=a+bx$

Now $x=1,y=7$ will satisfy above relation

$\Rightarrow 7=a+b$

$a+b=7$.......$\left(1\right)$

Also $x=2,y=6$ will satisfy above relation

$\Rightarrow 6=a+2b$

$a+2b=6$.....$\left(2\right)$

Solving $\left(1\right)$ and $\left(2\right)$, we get

$a=8,b=-1$

Hence $y=8-x$

So at $x=6$ $\Rightarrow y=8-6=2$.