The following table summarizes car sales by month.

a $-$ Determine the forecast for the months of July to December using the moving average based on $6$

months $($assume the current ones for the months of July to December as $12,16,15,11,19$ and $21).$

b$-$ Determine the forecast error for each month.

c $-$ Use the MAD to estimate the future error of the forecasts.

d$-$Explain the relationship of your prognosis with the result you obtained from the MAD.

Using the sales values from problem $1$

a $-$ Forecast through December with the three$-$month "Weighted Moving Average" with the following

weights:

b$-$Determine the forecast error per month.

c$-$ Determine variation with the MSE.

Using the sales values from problem $1$

a $-$ Forecast from July to December using exponential smootting with $a=0\mathrm{.}1.$ Assume the June

forecast is $16.$

b $-$ Determine the forecast error per month.

c $-$ What will be the percentage of variation using MAPE?

d $-$ Evaluate the forecast with $a=0\mathrm{.}8$ and $a=0\mathrm{.}5.$

e $-$ Which of the three alpha values would you choose to forecast?