FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 8.13Example10 :
Fit a straight line trend by the method of least squares taking year 2008 as origin, and estimate the sales for
the year 2012:
Year 2006 2007 2008 2009 2010 2011
Sales (crores) 24 26 28 30 44 52Solution:
Table : Straight line trend by Method of Least Squares
Year Sales (crores) Deviation X^2 XY
from 2002 (X)
2006 24 -2 4 -48
2007 26 -1 1 -26
2008 28 0 0 0
2009 30 1 1 30
2010 44 2 4 88
2011 52 3 9 156
ΣY=204 ΣX = 3 ΣX^2 = 19 ΣXY = 200
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
204 = 6a + 3b ......(1)
200 = 3a + 196 ......(2)
Multiplying equation (2) by 2 and subtracting from equation (2), we get
-196 = -35b
b = −−^13596 =5.6
Putting the value of b in equation 1
204 = 6a + 3 X (5.6)
204 = 6a + 16.8
6 a = 204-16.8
a = 187.2 6 =31.2
Equation for straight line trend is
Yc = 31.2 + 5.6 X (origin 2008)