FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 8.9Solve by :
(1) taking 2005 as the year of origin
(2) taking middle year of the time series as origin and also verify the result.
Solution:
Table (1) Trend by taking 2005 as origin
Year Exports Deviation X^2 XY
(in tons) (Y) from 2005 X
2003 47 -2 4 -94
2004 50 -1 1 -50
2005 53 0 0 0
2006 65 1 1 65
2007 62 2 4 124
2008 64 3 9 192
2009 72 4 16 288
ΣY = 413 ΣX = 07 ΣX^2 = 35 ΣXY = 525
Equation of a straight line trend is.
Yc = a+bX
To get the value of a and b, the following two normal equations have to be solved simultaneously—
ΣY = Na + bΣX
ΣXY = aΣX + bΣX^2
413 = 7a + 7 b ......(1)
525 = 7a + 356 .......(2)
Subtracting equation (1) from equation (2), we get
112 = 28b
b =^12812 = 4putting the value of b in equation 1
413 = 7a + 7 x 4
7 a = 413 - 28
7 a = 385
a =^3857 =^55
Equation for straight line trend is
Yc = 55 + 4X (origin 2005)
For 2005, X = 7
Yc = 55 + 4 X 7 = 55 + 28 = 83 tons