Montgomery et al$.(1990)$ give $4$ years of data on monthly demand for a soft drink. These data are given in Table E$4\mathrm{.}5.$

a$.$ Make a time series plot of the data and verify that it is seasonal. Why do you think seasonality is present in these data?

b$.$ UseWinters$$multiplicativemethodforthefirst$3$yearstodevelop a forecasting method for this data. How well does this smoothing procedure work?

c$.$ Make one$-$step$-$ahead forecasts of the last $12$ months. Determine the forecast errors. How well did your procedure work in fore$-$ casting the new data?