Questions:

$1.($a$)$ Linear Trend$-$find forecast for periods $16$ to $20($find the value of a and b followed by defining a linear trend equation, and then use it for forecasting periods $16$ to $10)$ and $($b$)$ Trend adjusted exponential smoothing, Use $=\mathrm{.}4$ and $=\mathrm{.}3-$ find forecast for period $16.(20$ points$)$

Use Excel to verify your answer $$ but show intermediate steps to receive full credit.

a$.$ t Y $($Data$)$ t$*$Y t$2$

$12002001$

$22144284$

$32116339$

$422891216$

$52351,17525$

$62221,33236$

$72481,73649$

$82502,00064$

$92532,27781$

$102672,670100$

$11281$

$12275$

$13280$

$14288$

$15310$

Part $($b$)$ Initial Trend $=$

Period Actual St$-1+$ Tt$-1=$ TAFt St $=$ TAFt $+\mathrm{.}4($A $$ TAFt$)$ Tt $=$ Tt$1+\mathrm{.}3($TAFt $$ TAFt$1$ Tt$1)$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$13$

$14$

$15$

$16$