Question

Suppose a firm is manufacturing automobiles and finds a relationship between sales of automobile and the index demand for cars. The sales for the last five years are

Year	2012	2013	2014	2015	2016
Sales (y)	110	130	150	160	180
Demand index (x)	100	110	140	150	200

Then the relationship between demand index and sales of automobile is

• A. y = 53.5 + 0.66 x
• B. y = 61.5 + 0.03 x
• C. y = 43.3 + 0.06 x
• D. y = 50.5 + 0.13 x

Answer 1

The correct option is A y = 53.5 + 0.66 x

Year	Demand (x)	Sales (y)	$x^2$	xy
2012 2013 2014 2015 2016	100 110 140 150 200	110 130 150 160 180	10000 12100 19600 22500 40000	11000 14300 21000 24000 36000
n = 5	$\sum$= 700	$\sum$y=730	$\sum x^2$=104200	$\sum$xy=106300

y = a + bx ...(1)
taking summation both side of equation

$\sum y=n.a+b\sum x$ ...(2)

Multiple equation (1) with x and then taking summation
$\sum xy=a\sum x+b\sum x^2$ ...(3)

By solving eq.(2) and (3)

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

$\Rightarrow a=53.5,b=0.66$
$\Rightarrow y=53.5+0.66x$