Question

Given data

x	1	3	4	6
y	1	2	4	4

Find the value of $m$ and $c$ for the equations of the lines of best fit for the regression analysis between $xandy$.

• A. $m=0.25,c=2.038$
• B. $m=0.3,c=3.038$
• C. $m=0.5,c=5.038$
• D. $m=0.65,c=4.038$

Answer 1

The correct option is D $m=0.65,c=4.038$

$x$	$y$	$xy$	$x^2$
$1$	$1$	$1$	$1$
$3$	$2$	$6$	$9$
$4$	$4$	$16$	$16$
$6$	$4$	$24$	$36$
$\sum x=14$	$\sum y=11$	$\sum xy=47$	$\sum x^2=62$

Here, $n=4$

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

$=\frac{4\times 47-14\times 11}{4\times 62-(14{)}^2}$

$=\frac{188-154}{248-196}$

$=\frac{34}{52}$

$=0.65$

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

$=\frac{14\times 62-47\times 14}{4\times 62-(14{)}^2}$

$=\frac{868-658}{248-196}$

$=\frac{210}{52}$

$=4.038$