Question

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

For the data, the slope and intercept for the line of best fit is

• A. $0.28,19$
• B. $1.28,-19$
• C. $1.48,-20$
• D. $2.28,-19$

Answer 1

The correct option is B $1.28,-19$

$x$	$y$	$xy$	$x^2$
$5$	$5$	$25$	$25$
$8$	$9$	$72$	$64$
$6$	$7$	$42$	$36$
$\sum x=19$	$\sum y=21$	$\sum xy=139$	$\sum x^2=125$

Here, $n=3$

$m=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x{)}^2}$

$=\frac{3\times 139-19\times 21}{3\times 125-(19{)}^2}$

$=\frac{417-399}{375-361}$

$=\frac{18}{14}$

$=1.28$

$c=\frac{\sum x\sum x^2-\sum xy\sum x}{n\sum x^2-(\sum x{)}^2}$

$=\frac{19\times 125-139\times 19}{3\times 125-(19{)}^2}$

$=\frac{2375-2641}{375-361}$

$=\frac{-266}{14}$

$=-19$