FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 8.7In such a case the values of a and b can be calculated as under—
Since ΣY = na,
a = ΣnY
Since ΣXY = bΣX^2 ,
b = ΣΣXYX 2
Example4 :
Fit a straight line trend to the following data by Least Square Method and estimate the sale for the year
2012 :
Year 2005 2006 2007 2008 2009 2010
Sale (in’000s) 70 80 96 100 95 114
Solution:
Table : Calculation of trend line
Year Sales Deviations from Deviations X^2 XY
Y 2007.5 multiplied by 2 (X)
2005 70 -2.5 -5 25 -350
2006 80 -1.5 -3 9 -240
2007 96 -.5 -1 1 -96
2008 100 +.5 +1 1 100
2009 95 +1.5 +3 9 285
2010 114 +2.5 +5 25 570
ΣY = 555 ΣX^2 = 70 ΣXY = 269
N = 6
Equation of the straight line trend is Yo = a + bX
Y (^555) 92.5
N 6
a=Σ = =
2
XY 269 3.843
70X
=Σ = =
b Σ∴ Trend equation is Yc = 92.5 + 3.843X
For 2012, X = 9
Y 2012 = 92.5 + 3.843 × 9 = 92.5 + 34.587
= 126.59 (in ‘000 `)