The following table shows the annual, inflation-adjusted profits of a bank in the years between 2005 to 2015 [in \(\$ 10^{6}\) ].

(1) Determine the smoothed values \(\left\{y_{i}\right\}\) obtained by applying M.A.(3).
(2) Based on the \(y_{i}\), determine the trend function (assumed to be a straight line).
(3) Draw the original time series plot, the smoothed version based on the \(y_{i}\), and the trend function in one and the same Figure.

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Year 1 (2005) 2 Profit xi 3 4 5 6 7 8 9 10 11 0.549 1.062 1.023 1.431 2.100 1.809 2.250 3.150 3.636 3.204 4.173