Problem $3$

You have realized that the sales for $12$ Rolls Select$-$A$-$Size Paper Towel have been increasing over the

past year. You have learned that the double exponential smoothing method can account for such a

trend in the data.

a$.$ Use double $($trend$-$adjusted$)$ exponential smoothing method to forecast sales for months $2$ to $13,$

assuming S$1=1306$ and T$1=15$ and set $\backslash$alpha $=0\mathrm{.}8$ and $\backslash$beta $=0\mathrm{.}2.$

b$.$ Plot the actual sales, the double exponential smoothing forecast, and the forecast obtained

using simple exponential smoothing in Problem $2$ with $\backslash$alpha $=0\mathrm{.}8$ for months $2$ to $12$ on the same

graph.

c$.$ Compute MAD and MAPE for months $2$ to $12$ for the double exponential smoothing forecast and

compare them with those of simple exponential smoothing in Problem $2($c$).$ Based on your

calculations, which approach is better in this particular case, single or double exponential

smoothing? Explain.

d$.$ Develop a simple linear regression model using month as the independent variable to forecast

the sales of $12$ Rolls Select$-$A$-$Size Paper Towel for month $13.$ Plot your regression forecasts

along with your double exponential smoothing forecasts for months $2$ through $13$ on the same

graph. Which one does seem to capture the sales trend better? Briefly explain why.