Question

For the given data the values of m and c of the normal equations of the line of best fit is.

X	11	7	9
Y	10	8	6

• A. $m=0.5,c=31.87$
• B. $m=0.6,c=34.00$
• C. $m=0.5,c=34.87$
• D. $m=0.8,c=33.87$

Answer 1

The correct option is C $m=0.5,c=34.87$

$x$	$y$	$xy$	$x^2$
$11$	$10$	$110$	$121$
$7$	$8$	$56$	$49$
$9$	$6$	$54$	$81$
$\sum x=27$	$\sum y=24$	$\sum xy=220$	$\sum x^2=251$

Here, $n=3$

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

$=\frac{3\times 220-27\times 24}{3\times 251-(27{)}^2}$

$=\frac{660-648}{753-729}$

$=\frac{12}{24}$

$=0.5$

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

$=\frac{27\times 251-220\times 27}{3\times 251-(27{)}^2}$

$=\frac{6777-5940}{753-729}$

$=\frac{837}{24}$

$=34.87$