Question

Study the following production data of a sugar factory.

Year	2001	2002	2003	2004	2005	2006	2007
Production (‘000 tonnes) (y)	76	87	95	81	91	96	90

 

What is the estimate of the production for 2008 using straight-line trend - with the origin at the year 2001 - by the least-squares method \((\sum x= 0, \sum x^2 = 28, \sum xy = 56) ?\)

1. 86
2. 88
3. 96
4. 98

Answer 1

Correct Answer - Option 3 : 96

Given

∑x = 0

∑x² = 28

∑xy = 56

Formula

a = ∑y/n

b = ∑xy/∑x²

Explanation

Year	y
2001	76
2002	87
2003	95
2004	81
2005	91
2006	96
2007	90
N = 7	∑y = 616

Y = a + bx

⇒ a = 616/7

⇒ a = 88

⇒ b = 56/28

⇒ b = 2

Y = 88 + 2x

⇒ X = 2008 – 2001 = 7

Y = 88 + 2 × 7

∴ estimate of the production for 2008 is 102