$1.$ Using the following methods forecast for all possible periods. Provide the report with appropriate interpretations for each forecast and show the graph of actual and forecast $(5$ points$)$

a$.$ Moving average $($n$=3)(1$ point$)$

b$.$ Exponential Smoothing $($alpha $=0\mathrm{.}6)(1$ point$)$

c$.$ Linear trend $($trend projection$)(1$ point$)$

d$.$ Linear regression $(2$ points$)$

$2.$ Discuss which method fits best for the bank$$s strategic plan to forecast the number of new accounts. You need to justify the selection of one method over another $(3$ points$).$

$3.$ Do you think that the exclusion of a part of data $($for example, the first $5-10$ years$)$ would affect the accuracy of the forecast? Briefly explain. Would such exclusion change your choice of the forecasting method in Question $2?$ Briefly explain $(2$ points$).$