$\backslash$table$[[$Period$,$t$,$Actual value $($A$)],[$Week $1,1,22],[$Week $2,2,26],[$Week $3,3,23],[$Week $4,4,27],[$Week $5,5,21],[$Week $6,6,25],[$Week $7,7,28],[$Week $8,8,26],[$Week $9,9,29],[$Week $10,10,29],[$Week $11,11,27],[$Week $12,12,31]]$

a$.$ Write down the forecast $)$ for Week $13$ using a $3$week weighted moving average, with weights $5,3,1($with $5$ being applied to the most recent value, then $3,$ then $1).$

b$.$ Write down the forecast $(F_{13})$ for Week $13$ using exponential smoothing with alpha $=\mathrm{.}45.$ Please start the forecast at Week $1,$ with Week $1$ actual number sold $)=(22$ and the forecast for Week $)=(22,$ then continue through Week $13$ to find $F_{13}$

c$.$ Create forecasts for all possible time periods $($not just Week $13)$ using the above methods $($weighted moving average $-$ Weeks $4-12,$ exponential smoothing $-$ Weeks $1-12).$

Then calculate errors $($E$)$ for each forecast method for the time periods $4-12($Week $4,5,6,...,12).$ Then use these error terms to calculate the MAD, MSE, and MAPE for each forecast method.

d$.$ Which method do you think is best and why?