Question

Find the equation of $y$ on $x$ for the following data

$x$	$8$	$6$	$4$	$7$	$5$
$y$	$9$	$8$	$5$	$6$	$2$

• A. $y=2x-1.2$
• B. $y=1.2x+1.2$
• C. $y=1.2x-1.2$
• D. $y=1.2x-2$

Answer 1

The correct option is C $y=1.2x-1.2$

$x$	$y$	$x^2$	$x\times y$
$8$	$9$	$64$	$72$
$6$	$8$	$36$	$48$
$4$	$5$	$16$	$20$
$7$	$6$	$49$	$42$
$5$	$2$	$25$	$10$

$\sum x=30$
$\sum y=30$
$\sum x^2=190$
$\sum x\times y=192$
So, $\overline{x}=\frac{\sum x}{n}=\frac{30}{5}=6$
$\overline{y}=\frac{\sum y}{n}=\frac{30}{5}=6$
$b_{yx}=\frac{\sum xy-\frac{\sum x\times \sum y}{n}}{\sum x^2-\frac{(\sum x{)}^2}{n}}=\frac{192-180}{190-180}=\frac{12}{10}=1.2$
Regression line of y on x will be $y-\overline{y}=b_{yx}(x-\overline{x})$
$y-6=1.2(x-6)$
$y=1.2x-7.2+6$
$y=1.2x-1.2$