The gift shop is currently preparing a forecast plan for next year. The manager is considering the best forecast method. Sales for the past $10$ months for hoodies are listed below.

$\backslash$table$[[$Month$,$Demand$],[1,114],[2,120],[3,125],[4,116],[5,137],[6,120],[7,115],[8,127],[9,119],[10,127]]$

Note: For each forecasting procedure, calculate $($keep one decimal$)$:

i$.$ the cumulative sum of forecast error $($CFE$),$

ii$.$ the mean absolute deviation $($MAD$),$

iii. the standard deviation of the errors,

a$.$ Calculate forecasts using na$$ve forecasting method for periods $4$ through $10.$

b$.$ Three$-$period moving$-$average forecast for periods $4$ through $10.$

c$.$ For periods $4$ through $10,$ develop the exponentially smoothed forecasts using a forecast for period $3(F_3)$ of $120\mathrm{.}0$ and an alpha of $0\mathrm{.}2.$

d$.$ For periods $4$ through $10,$ do trend projection $($hint: use Excel for the regression equation$)$

e$.$ Which forecasting procedure would you select? Why?