Use these data and your computer to prepare a managerial report $(10$ points$)$ along the following guidelines:

$1.$ Use exponential smoothing to develop simple, trend $($Holt$\text{'}$s$),$ and seasonal models $($both simple and trend$)$ for forecasting the quarterly revenue from $2-$year plans. Do the same for $5-$year plans, and also for the total revenue. Use the RMSE performance measure for selecting the best model in each case. $(40$ points$)$

$2.$ Use the three best models you obtained in guideline $1$ to forecast total revenue and revenues from each individual type of plan in the next four $(4)$ quarters. Create $\backslash (99\backslash \%\backslash )$ confidence intervals for each forecast. $(\backslash (\backslash$mathbf$\{10\}\backslash )$ points$)$

$3.$ When you showed these results to Ms$.5$G$,$ she pointed out that the sum of the forecasts for sales from the two plans is not equal to the forecast of the total revenue. To achieve consistency in these forecasts, your staff proposed the following approaches.

a$.$ Use the best models you obtained in guideline $1$ for forecasting the revenues from each of the two types of plans. Then, forecast the total revenue as the sum of these two forecasts. With this method, what forecast would you obtain for the total revenue in each of the last eight $(8)$ quarters? Compare these forecasts to the actual total revenues, and compute the resulting RMSE measure. $(10$ points$)$

b$.$ Mr$.$ Alvarez from your staff noted that, on the basis of the historical data, the average percentage of total revenue contributed by $2-$year plans is about $\backslash (33\mathrm{.}5\backslash \%\backslash ),$ and that contributed by $5-$year plans is $\backslash (66\mathrm{.}5\backslash \%\backslash ).$ He proposed using the best model you obtained in guideline $1$ for forecasting the total revenue, and then forecasting the individual plan sales by multiplying the forecast of the total revenue by the percentage contributed by that type of plan. With this method, what forecast would you obtain for the revenue from each of the two individual types of plans in each of the last eight $(8)$ quarters? Compare these forecasts to the actual revenues, and compute the resulting RMSE measure for each type of plan. $(\backslash (\backslash$mathbf$\{10\}\backslash )$ points$)$ THE FORECASTING PROBLEM OF AMERICAN MOBILE

The management of American Mobile is having a meeting to plan the operating budgets for next year. The Senior Vice$-$President of Sales, Ms$.$ Angela $5$G$,$ knows that a large portion of the company's income is derived from sales of their $2-$year and $5-$year plans. She has asked you, Manager of Sales and current QMB $612$ Candidate, to prepare an estimate of the revenues the company can expect in each of the next four quarters from $2-$year and $5-$year plans, as well as the total revenue from both of these plans.

To prepare your forecast, you have contacted Mr$.$ Sheep in the Accounting Department, who has provided you with the following sales figures $($in $\backslash (\backslash$$ $\backslash )$ thousands$)$ from the last $16$ quarters:

c$.$ Compare and discuss the two approaches in parts $($a$)$ and $($b$)$ by preparing a summary table of the RMSE measures for forecasting the revenues from the two types of plans and the total revenue. Discuss the advantages and disadvantages of each method. $(10$ points$)4.$ Develop a linear fit model using time as the independent variable for forecasting the quarterly revenue from $2-$year plans. Do the same for $5-$year plans, and also for total revenue. How do the forecasting performances of these linear fit models compare with the exponential smoothing models developed in guideline $1?(10$ points$)$