$(1)$ Obtain the linear trend equation for the following data on new checking accounts at Fair

Saving Bank and use it to predict new checking accounts for periods $16$ to $19.$

Period New Accounts Period New Accounts Period New Accounts

$1200623211281$

$2214724812275$

$3211825013280$

$4228925314288$

$52351026715310$

$(2)$ Use Holt$$s method with $4=228,4=9\mathrm{.}33,=0\mathrm{.}3$ and $=0\mathrm{.}2$ to smooth the new

account data in part $(1).$ What is the forecast for period $16?$