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:

$\backslash$table$[[$Month$,\backslash$table$[[$Actual Sales$],[($Smillion$)]],\backslash$table$[[$Forecast$],[($Smillion$)]],,,],[1,22,30,,,],[2,22,24,,,],[3,22,18,,,],[4,22,15,,,],[5,24,15,,,],[6,24,19,,,],[7,24,24,,,],[8,23,26,,,],[9,23,32,,,],[10,23,27,,,],[11,23,22,,,],[12,22,16,,,],[13,22,14,,,],[14,22,18,,,],[15,22,21,,,],[16,21,23,,,],[17,21,25,,,],[18,20,28,,,],[19,20,25,,,],[20,20,21,,,],[,,,,,]]$

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 $-\mathrm{.}1.$ What can you conclude? Assume limits of $\frac{+}{-}4.$

b$).$ Using the first half of the data construct a control chart with $2s$ limits$,$ What can you conclude?

c$).$ Plot the last $10$ errors on the control chart. Are the errors random? What is the implication of this?

Ch $3\_$Forecasting$\_$Tracking Signals$\_$Mad$\_$Exponential Smoothing$\_$Control Charts