Consider the following partially filled forecast table made by a consumer electronics retailer about the

average number of employees in outlets. The forecast was made by utilizing single exponential smoothing

method with an alpha $(??)=0\mathrm{.}1.$ ?Answer the following question based on the time series plot and partially

completed table.

Year

Avg. no $.$ ?of

employees Forecast

Absolute

Forecast

Error

$120\mathrm{.}6020\mathrm{.}60$

$217\mathrm{.}3020\mathrm{.}603\mathrm{.}30$

$318\mathrm{.}6020\mathrm{.}271\mathrm{.}67$

$421\mathrm{.}5020\mathrm{.}101\mathrm{.}40$

$523\mathrm{.}2020\mathrm{.}242\mathrm{.}96$

$619\mathrm{.}9020\mathrm{.}540\mathrm{.}64$

$718\mathrm{.}7020\mathrm{.}471\mathrm{.}77$

$815\mathrm{.}6020\mathrm{.}304\mathrm{.}70$

$919\mathrm{.}7019\mathrm{.}830\mathrm{.}13$

$1020\mathrm{.}4019\mathrm{.}810\mathrm{.}59$

$11?$

alpha $=0\mathrm{.}1$ ?SUM $=17\mathrm{.}15$

MAD $=?$

a $)$ ?Based on the time series plot of actual values, does it appear that a linear trend exists in the time

series?

b $)$ ?Calculate the forecast for year $11$ ?based on the smoothing constant $($ alpha $)=0\mathrm{.}1.$

c $)$ ?Calculate the mean absolute deviation $($ MAD $)$ ?for this forecasting model.

d $)$ ?Assume for alpha $=0\mathrm{.}5,$ ?the MAD equaled $2\mathrm{.}35.$ ?Which value of smoothing constant $($ alpha $=0\mathrm{.}1$ ?vs

alpha $=0\mathrm{.}5)$ ?would be more appropriate for forecasting?

$15\mathrm{.}00$

$20\mathrm{.}00$

$25\mathrm{.}00$

$12345678910$

Avg. no $.$ ?of Employees

Year