Question

Suppose a firm has had the historical sales figures shown as follows. What would be the forecast for next year's sales using regression to estimate a trend?

Year		2008				2009				2010				2011				2012
Sales		$	2,000,000			$	1,800,000			$	2,200,000			$	2,400,000			$	2,300,000

Multiple Choice

• $2,140,000

• $2,225,000

• $2,300,000

• $2,500,000

Answer 1

Let x be the years denoted by 1-5

Let y be the sales

Let the Regression line be y = b_o + b₁x

where,

b_o = ( Σy Σx² - Σx Σxy ) / ( nΣx² - (Σx)² )

b₁ = ( nΣxy - ΣxΣy ) / ( nΣx² - (Σx)² )

	Year(x)	Sales(y)	x2	xy
	1	2000000	1	2000000
	2	1800000	4	3600000
	3	2200000	9	6600000
	4	2400000	16	9600000
	5	2300000	25	11500000
Σ	15	10700000	55	33300000

b_o = ( 10700000*55 - 15*33300000 ) / ( 5*55 - 15² ) = 1780000

b₁ = ( 5*33300000 - 15*10700000 ) / ( 5*55 - 15² ) = 120000

Hence, y = 1780000 + 120000x

Hence, for 2013, x = 6 => y = 1780000 + 120000*6 = 2500000

Hence, (d) $2500000 is the correct option