FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 8.11The equation of the straight line trend is
Yc = a + bX
Since ΣX = 0; a = ΣN NY 102= =^7
b = 2
XY 98 1.4
X 70
Σ = =
Σ
The trend line is Yc = 17 + 1.4X
(ii) For 2012 X = 7, so Y 2012 = 17 + 1.4(7) =17 + 9.8
Y = 26.8
[Note: The deviations are taken from the middle year 2008.5 to reduce the calculations & then the resultant
figures are multiplied by 2, to make calculations less cumbersome]
Example8 :
Below are given the figures of sales in thousand quintals of a firm operating in the sugar industry :
Year 2001 2003 2005 2007 2009
Sales in’000 quintals 70 90 100 130 170
(i) Fit straight line trend to these figures using the least squares method
(ii) Estimate the sales of the firm for the year 2012
(iii) What is the annual increase or decrease in the expected sales of the firm?
Solution:
(i) Table : Calculation of Trend & Trend Values
Year Sales in ‘000 Deviations from X^2 XY
quintals (Y) 2005 (X)
2001 70 -4 16 -280
2003 90 -2 4 -180
2005 100 0 0 0
2007 130 2 4 260
2009 170 4 16 680
ΣY= 560 0 ΣX^2 =40 ΣXY=480
The equation of the straight line trend is
Yc = a + bX
Since ΣX = 0; a = ΣN 5Y=^560 =^112
b = ΣΣXXY 480 2 = 40 =^12
The trend line is Yc = 112 + 12X