Ch $3$: Forecasting: Tracking Signals, Mad, Exponential Smoothing, Control Charts Media Consultants $(10$ Pts$).$

Media Consultants uses proven techniques to measure forecast accuracy and to determine when the forecast needs to be reviewed$/$updated$.$

The following data has been extracted from their information system:

Month

Actual Sales $($$million$)$

Forecast $($$million$)$

$1$

$22$

$30$

$2$

$22$

$24$

E

$22$

$18$

$4$

$22$

$15$

$5$

$24$

$15$

$6$

$24$

$19$

$7$

$24$

$24$

$23$

$26$

$9$

$23$

$32$

$10$

$23$

$27$

$11$

$23$

$22$

$12$

$22$

$16$

$13$

$22$

$14$

$14$

$22$

$18$

$15$

$22$

$21$

$16$

$21$

$23$

$17$

$21$

$25$

$18$

$20$

$28$

$19$

$20$

$25$

$20$

$20$

$21$

a$).$ Compute a tracking signal for months $11$ through $20.$ Compute an initial value of MAD for month $11,$ and then update it for each month using exponential smoothing with alpha$-1.$ What can you conclude? Assume limits of $+/-4.$