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Obtain trend values for data, using 4yearly centred moving averages
Year  1971  1972  1973  1974  1975  1976 
Production  1  0  1  2  3  2 
Year  1977  1978  1979  1980  1981  1982 
Production  4  6  5  1  4  10 
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Solution
Construct the following table for obtaining 4yearly centred moving average for the data.
Year t 
Production y_{t} 
4yearly moving

4yearly moving average  2 unit moving total  4yearly centred moving averages trend value 
1971  1  
1972  0  
4  1  
1973  1  2.5  1.25  
6  1.5  
1974  2  3..5  1.75  
8  2  
1975  3  4.75  2.375  
11  2.75  
1796  2  6.5  3.25  
15  3.75  
1977  4  8  4  
17  4.25  
1978  6  8.25  4.125  
16  4  
1979  5  8  4  
16  4  
1980  1  9  4.5  
20  5  
1981  4  
1982  10 
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0  0  1  1  2  3  4  5 
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1990  5  – 1  1  – 5 
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2005  1  2  4  2 
2010  0  3  9  0 
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Σy = na + bΣx
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2008  14  – 5  25  – 70 
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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 
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