You are the operations chief for the Silver Spring Fire Department, which is deciding whether to buy another fire engine $($this is a real situation$).$ The decision will rest partly on the anticipated number of emergency calls to which the truck will respond next year. The calls during the past seven years are as follows:

$2017$

$1060$

$2018$

$1387$

$2019$

$1291$

$2020$

$1343$

$2021$

$1404$

$2022$

$1491$

$2023$

$1609$

a$)$ Forecast the number of calls for this year using a $3-$year moving average

b$)$ Find the MAD for your forecast in $($a$)$

c$)$ Use a weighted $3$ year moving average with weights of $0\mathrm{.}2,0\mathrm{.}3$ and $0\mathrm{.}5$ to forecast next year's number of calls. $($The weight of $0\mathrm{.}5$ is for the most recent year$)$

d$)$ What is the MAD for this weighted forecast?

e$)$ Compute the forecast for $2024$ using exponential smoothing, an initial forecast of $1200$ emergency

responses in $2017,$ and a $=0\mathrm{.}3.$

$+)$

What if you try it again with a $=0\mathrm{.}4?$

g$)$ Which of these several forecasts is best, and why?

h$)$ Speculate: Why might there be an upward trend in number of calls?