8.14 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSTime Series Analysis
For 2012, X = 4
Yc = 31.2 + 5.6 X 4 = 31.2 + 22.4 = 53.6
Thus, the estimated, sales for the year 2012 is 53.6 crores.
Example 11:
Fit a straight line trend to the following data by least squares method :
2001 2003 2005 2007 2009
18 21 23 27 16
(i) Estimate sales for the year 2012.
(ii) What is the annual increase/decrease in the trend values of sales?
Solution:
Table : Least Squares Method
Exports Deviation X^2 XY
(in tons) from 2005 X
2001 18 -4 16 -72
2003 21 -2 4 -42
2005 23 0 0 0
2007 27 2 4 54
2009 16 4 16 64
ΣY=105 ΣX = 0 ΣX^2 = 40 ΣXY = 4
(i) The equation of the straight line trend is
Yc = a + bX
Since ΣX = 0; a = ΣN 5Y 105= =^21b = ΣΣXY 4X 2 = 40 =0.1
The trend line is Yc = 21 + 0.1X (origin 2005)
For 2012 X = 7, so Y 2012 = 21 + 0.1(7) = 21 +0.7
Y = 21.7
The expected sales for the year 2012 is ` 21.7 lakh
(ii) The annual increase in the trend values of sales (as given by b) is ` 0.1 lakh i.e. ` 10,000.
SELF EXAMINATION QUESTIONS
Problem 1: What are the different components of a time series? Describe briefly each of these
components?
Problem 2: Briefly describe various components of time series. Give the additive & multiplicative
models of time series.
Problem 3: What is ‘secular trend? What is the use of studying it? List two methods of measuring
trend.