QUESTION $2(25$ Marks$)$

Forecasting as highlighted by Heizer and Render $(2014)$ is the science of predicting future events and may be based on

historical and demand driven data.

$2\mathrm{.}1$ Identify and analyse the features that distinguish medium and long range forecasts from short range forecasts.

$(10$ marks$)$

$2\mathrm{.}2$ The information provided relates to the room registrations at Msisi Hotel for the past $8$ years. In order to project

future demand the management is interested in determining the mathematical trend of guest registration. This will

help the management in determining whether future expansion is warranted.

Table $1\mathrm{.}1$: Msisi Hotel Registrations

Year $($x$)$ Room Registrations $($y$)$

$117$

$216$

$316$

$421$

$520$

$620$

$723$

$825$

i$.$ Given the data on Table $1\mathrm{.}1,$ develop a least squares equation $($trend equation$)$ relating room registrations to

time. $(11$ marks$)$

ii$.$ What would be the forecasted room registrations for year $9?$