Paper 4: Fundamentals of Business Mathematics & Statistic

8.8 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Time Series Analysis

Example 5:

Fit a straight line trend to the following data and estimate the likely profit for the year 2012. Also calculate

the trend values.

Year 2003 2004 2005 2006 2007 2008 2009

Profit (in lakhs of `) 60 72 75 65 80 85 95

Solution:

Table : Calculation of Trend and Trend Values

Year Profit Deviation X^2 XY Trend Values

Y from 2006 (Yc = a + bX)

X [Yc= 76 + 4.85X]

2003 60 -3 9 -180 76 + 4.85 (-3) = 61.45

2004 70 -2 4 -144 76 + 4.85 (-2) = 66.30

2005 75 -1 1 -75 76 + 4.85 (-1) = 70.15

2006 65 0 0 0 76 + 4.85 (0) = 76

2007 80 1 1 80 76 + 4.85(1) = 80.85

2008 85 2 4 170 76 + 4.85 (2) = 85.70

2009 95 3 9 285 76 + 4.85 (3) = 90.55

Σy = 532 ΣX^2 = 28 ΣXY=136

N = 7

The equation for straight line trend is Yc = a + bX

Where

Σx = 0; a = ΣN 7Y=^532 =^76

b = ΣΣXY 136X 2 = 28 =4.85

yc = 76 + 4.85X

For 2012, x = 6 (2012 - 2006)

yc= 76 + 4.85(6) = 76 + 29.10

= 105.10

The estimated profit for the year 2012 is ` 105.10 lakhs.

Example6 :

Fit a straight line trend to the following data by Least Squares method and estimate exports for the year

2012.

Year 2003 2004 2005 2006 2007 2008 2009

Exports (in tons) 47 50 53 65 62 64 72