Extrapolation
The Extrapolation refers to estimating a value for the future period. In order to extrapolate a particular value, the various techniques discussed for interpolation can be adopted. The choice of particular technique would depend upon: (a) the requirement of the question, and (b) the nature of the data given.
Illustration: Extrapolate the business done in 2008 from the following data:
|
Year
|
2003
|
2004
|
2005
|
2006
|
2007
|
|
Business done ($ 0.1 millions)
|
150
|
235
|
365
|
525
|
780
|
Solution:
We can extrapolate the business done in 2008 by the Binomial expansion method. Since the known values are five, the fifth leading differences will be zero, i.e. (y - 1)5 = 0 or Δ05 = 0
Δ05 = y5 - 5y4 + 10y3 - 10y2 + 5y1 - y0 = 0
|
X
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
|
Y
|
150
|
235
|
365
|
525
|
780
|
?
|
|
|
y0
|
y1
|
y2
|
y3
|
y4
|
y5
|
We have to find the value of y5
(y - 1)5 = y5 - 5 (780) + 10 (525) - 10 (365) + 5 (235) - 150 = 0
= y5 - 3900 + 5250 - 3650 + 1175 - 150 = 0
-y5 = 3900 - 5250 + 3650 - 1175 + 150
-y5 = -1275 or y5 = 1275