Question

Find the line of regression of $y$ on $x$ for the following data:

$x$	$y$
$10$	$8$
$9$	$12$
$8$	$7$
$7$	$10$
$6$	$9$
$5$	$6$

Answer 1

$x$	$y$	$xy$	$x^2$	$y^2$
10	8	80	100	16
9	12	108	81	144
8	7	56	64	49
7	10	70	49	100
6	8	48	36	64
4	9	36	16	81
3	6	18	9	36
$\sum x=47$	$\sum y=60$	$\sum xy=416$	$\sum x^2=355$	$\sum y^2=490$

Here $n=7$
$b_{yx}=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum {x)}^2}$
$=\frac{7\times 416-(47\times 60)}{7\times 355-{\left(47\right)}^2}=0.3333$
Now, $\overline{x}=\frac{\sum x}{7}=\frac{47}{7}=6.71$
$\overline{y}=\frac{\sum y}{7}=\frac{60}{7}=8.57$
The line regression on $x$ is:
$y-\overline{y}=b(x-\overline{x})$
$y-8.57=0.33(x-6.71)$
$y=0.33x-2.214+8.57$
$y=0.33x+6.36$