# Fit equation of trend line for the data given below. Year Production (y) x x2 xy 2006 19 – 9 81 – 171 2007 20 – 7 49 – 140 2008 14 – 5 25 – 70 2009 16 – 3 9 – 48 2010 17 – 1 1 – 17 2011 16 1 1 16 201 - Mathematics and Statistics

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Fit equation of trend line for the data given below.

 Year Production (y) x x2 xy 2006 19 – 9 81 – 171 2007 20 – 7 49 – 140 2008 14 – 5 25 – 70 2009 16 – 3 9 – 48 2010 17 – 1 1 – 17 2011 16 1 1 16 2012 18 3 9 54 2013 17 5 25 85 2014 21 7 49 147 2015 19 9 81 171 Total 177 0 330 27

Let the equation of trend line be y = a + bx   .....(i)

Here n = square (even), two middle years are square and 2011, and h = square

The normal equations are Σy = na + bΣx

As Σx = 0, a = square

Also, Σxy = aΣx + bΣx2

As Σx = 0, b = square

Substitute values of a and b in equation (i) the equation of trend line is square

To find trend value for the year 2016, put x = square in the above equation.

y = square

#### Solution

Let the equation of trend line be y = a + bx   .....(i)

Here n = 10 (even), two middle years are 2010 and 2011, and h = 2

The normal equations are Σy = na + bΣx

As Σx = 0,

∴ 177 = 10a + b(0)

∴ a = 177/10

a = 17.7

Also, Σxy = aΣx + bΣx2

As Σx = 0,

27 = a(0) + b(330)

∴ b = 27/330

= 0.08

b = 0.1

Substitute values of a and b in equation (i) the equation of trend line is y = 17.7 + 0.1x

To find trend value for the year 2016, put x = 11 in the above equation.

y = 17.7 + 1.1

y = 18.8

Concept: Measurement of Secular Trend
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Chapter 2.4: Time Series - Q.5
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