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The following table shows gross capital information (in Crore ₹) for years 1966 to 1975: Years 1966 1967 1968 1969 1970 Gross Capital information 20 25 25 30 35 Years 1971 1972 1973 1974 1975 - Mathematics and Statistics

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Question

The following table shows gross capital information (in Crore ₹) for years 1966 to 1975:

Years 1966 1967 1968 1969 1970
Gross Capital information 20 25 25 30 35
Years 1971 1972 1973 1974 1975
Gross Capital information 30 45 40 55 65

Obtain trend values using 5-yearly moving values.

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Solution

Year Yt 5-yearly
moving total
5-yearly
moving
averages
(trend value)
1966 20
1967 25
1968 25 135 27
1969 30 145 29
1970 35 165 33
1971 30 180 36
1972 45 205 41
1973 40 235 47
1974 55
1975 65
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Measurement of Secular Trend
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2022-2023 (March) Official

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2006 19  
    `square`    
2007 20   `square`
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2008 17   142 17.75
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2009 16   `square` 17
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2011 16   `square` `square`
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2014 21  
       
2015 19  

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Solution:

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2010 3 3 -2 4 -6
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2016 4 9 4 16 16
  `sumx_t=68` - `sumu=0` `sumu^2=60` `square`

The equation of trend is xt =a'+ b'u.

The normal equations are,

`sumx_t=na^'+b^'sumu             ...(1)`

`sumux_t=a^'sumu+b^'sumu^2      ...(2)`

Here, n = 9, `sumx_t=68,sumu=0,sumu^2=60,sumux_t=-44`

Putting these values in normal equations, we get

68 = 9a' + b'(0)     ...(3)

∴ a' = `square`

-44 = a'(0) + b'(60)          ...(4)

∴ b' = `square`

The equation of trend line is given by

xt = `square`


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