Question

For the given data:

X	8	9	11	14
Y	5	7	8	9

Find the values of m and c for the normal equations of the line of best fit.

• A. $m=0.59,c=72.5$
• B. $m=0.9,c=62$
• C. $m=0.50,c=62$
• D. $m=0.4,c=52$

Answer 1

Answer: (A)

$m=0.59,c=72.5$

$x$	$y$	$xy$	$x^2$
$8$	$5$	$40$	$64$
$9$	$7$	$63$	$81$
$11$	$8$	$88$	$121$
$14$	$9$	$126$	$196$
$\sum x=42$	$\sum y=29$	$\sum xy=317$	$\sum x^2=462$

Here, $n=4$

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

$=\frac{4\times 317-42\times 29}{4\times 462-(42{)}^2}$

$=\frac{1268-1218}{1848-1764}$

$=\frac{50}{84}$

$=0.59$

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

$=\frac{42\times 462-317\times 42}{4\times 462-(42{)}^2}$

$=\frac{19404-13314}{1848-1764}$

$=\frac{6090}{84}$

$=72.5$