Data $($shown in below table$)$ for the past $8$ quarters at the Port of Vancouver has unloaded large quantities of Wheat grain from the cargo ship MV Ocean Breeze. The port operation manager wants to test the use of exponential smoothing method to see how well the technique works in predicting tonnage unloaded. He guesses that forecast of grain unloaded in the first quarter was $175$ tons. Two values of $\backslash$alpha are to be examined: $\backslash$alpha $=0\mathrm{.}10$ and $\backslash$alpha $=0\mathrm{.}50.$

Quarter Actual Tonnage Unloaded

$1180$

$2168$

$3159$

$4175$

$5190$

$6205$

$7180$

$8182$

$9?$

Question$1.$ Compare the actual data with the data we forecast $($using of the two $\backslash$alpha values$)(2\mathrm{.}5$ marks$).$

Question $2.$ By using of the two $\backslash$alpha values, find the mean absolute deviation and MADs. On the basis of this comparison of the two MADs, which $\backslash$alpha value is preferred? $(2\mathrm{.}5$ marks$).$

Question $3.$ From the above table compute the MSE $($Mean Squared Error$)($use the same forecast data for $\backslash$alpha $=0\mathrm{.}10.$ Provide justification for your answer of MSE good or bad? $(2\mathrm{.}5$ marks$).$

Question $4.$ Now calculate the MAPE $($Mean Absolute Error$)$ when $\backslash$alpha $=0\mathrm{.}10(2\mathrm{.}5$ marks$).$