Question $3(8$ points$)$

The car dealer wants to forecast the demand accurately. From sales records, the dealer has accumulated the following data for the year $2023($also available in the "exam $3$ data spring $2024.$xls$"$ file tab Q$3).$

Month Sales

June $18$

July $35$

August $20$

September $25$

October $30$

November $40$

$($a$)$ Compute $3-$month moving average forecasts $($i$.$e$.,$ with a span of $3$ months$)$ of sales for September $2023$ to December $2023.$

$($b$)$ Compute exponential smoothing forecasts for July $2023$ to December $2023$ with the smoothing constant $\backslash$alpha to be $0\mathrm{.}4.($Hint: Initialize the forecast for June $2023$ as $18.)$

$($c$)$ Which method is better based on MAD?