An agricultural institute is interested in analysing the pattern of the employment in agriculture in a particular state in past years and then forecasting the expected number of employment for the upcoming years. The number of persons (in millions) employed in agriculture on a monthly basis from January 2008 through December 2017. The
following monthly data are available for past 10 years:
| Year | ||||||||||
| Month | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |
| January | 2.877 | 2.869 | 2.955 | 3.197 | 2.888 | 2.853 | 2.672 | 2.868 | 2.762 | 2.782 |
| February | 2.846 | 2.909 | 2.956 | 3.283 | 2.89 | 2.802 | 2.709 | 2.771 | 2.796 | 2.836 |
| March | 3.042 | 3.094 | 3.131 | 3.334 | 2.988 | 2.897 | 2.804 | 2.913 | 2.925 | 2.962 |
| April | 3.505 | 3.287 | 3.295 | 3.437 | 3.171 | 3.273 | 3.14 | 3.151 | 3.074 | 3.081 |
| May | 3.598 | 3.531 | 3.467 | 3.604 | 3.622 | 3.415 | 3.478 | 3.369 | 3.309 | 3.436 |
| June | 3.92 | 3.976 | 4.053 | 3.895 | 3.869 | 3.78 | 3.82 | 3.983 | 3.785 | 3.737 |
| July | 3.971 | 4.061 | 4.165 | 4.024 | 4.09 | 3.931 | 3.79 | 3.997 | 3.857 | 3.853 |
| August | 3.764 | 4.031 | 3.826 | 3.851 | 3.886 | 3.842 | 3.682 | 3.856 | 3.795 | 3.636 |
| September | 3.444 | 3.658 | 3.436 | 3.563 | 3.626 | 3.396 | 3.326 | 3.549 | 3.545 | 3.635 |
| October | 3.47 | 3.721 | 3.525 | 3.536 | 3.524 | 3.447 | 3.408 | 3.553 | 3.467 | 3.501 |
| November | 3.262 | 3.363 | 3.419 | 3.224 | 3.156 | 3.081 | 3.181 | 3.1 | 3.257 | 3.214 |
| December | 2.948 | 3.163 | 3.202 | 2.959 | 2.856 | 2.85 | 2.914 | 2.99 | 2.995 | 3.057 |
a) Compute the seasonal indices using ratio to moving average method.
b) Obtain the deseasonalised values and then fit a linear trend line to the average annual employment using least squares method.
c) Convert the annual least-squared trend equation to a monthly trend equation.
d) Use the monthly trend equation and seasonal indices to forecast the number of persons employed in agriculture for all twelve months of 2018 and 2019.
e) Plot the original data, deseasonalised data and trend values.
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