Part $($a$)$ Develop a seasonally adjusted forecast model in excel for seat occupancy. Forecast seat occupancy for year $6$ by using a linear trend line forecast estimate for seat occupancy in year $6.$

Part $($b$)$ Develop linear regression models in excel relating seat occupancy to discount fares in order to forecast seat occupancy for EACH QUARTER separately in year $6.$ Assume a fare discount of $20\%$ for quarter $1,36\%$ for quarter $2,25\%$ for quarter $3,$ and $30\%$ for quarter $4.$

Part $($c$)$ Compare the forecasts developed in $($a$)$ and $($b$)$ and indicate which one appears to be the best. Just an intuitive assessment would be enough.

Part $($d$)$ Develop an adjusted exponential smoothing forecast model $($alpha $=\mathrm{.}40$ and beta $=\mathrm{.}40)$ for the quarterly data to forecast seat occupancy and compare its accuracy with the seasonally adjusted model developed in $($a$),$ using a forecast accuracy measure $($e$.$g$.,$ MAD$).$ Note that you must use the quarterly data $($not aggregated annual data$)$ and you can only estimate the seat occupancy for the first quarter of year $6.$

Bonus $(5$pts$)$:$$Find the optimal value of alpha and beta in part $($d$)$ that minimizes the sum of squared errors.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Year & Quarter & $\backslash [$

$\backslash$begin$\{$array$\}\{$c$\}$

$\backslash$text $\{$ Seat $\}\backslash \backslash$

$\backslash$text $\{$ Occupancy $\}\backslash \backslash$

$\backslash$text $\{(\backslash \%)\}$

$\backslash$end$\{$array$\}$

$\backslash ]$ & Average Fare Discount $(\backslash \%)\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$t$]\{4\}\{*\}\{1\}$ & $1$ & $63$ & $21\backslash \backslash$

$\backslash$hline & $2$ & $75$ & $34\backslash \backslash$

$\backslash$hline & $3$ & $76$ & $18\backslash \backslash$

$\backslash$hline & $4$ & $58$ & $26\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$t$]\{4\}\{*\}\{2\}$ & $1$ & $59$ & $18\backslash \backslash$

$\backslash$hline & $2$ & $62$ & $40\backslash \backslash$

$\backslash$hline & $3$ & $81$ & $25\backslash \backslash$

$\backslash$hline & $4$ & $76$ & $30\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$t$]\{4\}\{*\}\{3\}$ & $1$ & $65$ & $23\backslash \backslash$

$\backslash$hline & $2$ & $70$ & $28\backslash \backslash$

$\backslash$hline & $3$ & $78$ & $30\backslash \backslash$

$\backslash$hline & $4$ & $69$ & $35\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$t$]\{4\}\{*\}\{4\}$ & $1$ & $59$ & $20\backslash \backslash$

$\backslash$hline & $2$ & $61$ & $35\backslash \backslash$

$\backslash$hline & $3$ & $83$ & $26\backslash \backslash$

$\backslash$hline & $4$ & $71$ & $30\backslash \backslash$

$\backslash$hline $\backslash$multirow$[$t$]\{4\}\{*\}\{5\}$ & $1$ & $60$ & $25\backslash \backslash$

$\backslash$hline & $2$ & $66$ & $37\backslash \backslash$

$\backslash$hline & $3$ & $86$ & $25\backslash \backslash$

$\backslash$hline & $4$ & $74$ & $30\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$