Question $2$

Demand for video projectors from a reputed company over the last two years is shown in Table $2.$ The company is trying to forecast the demand for the year of $2022.$

Table $2$: Monthly Demand for Video Projectors

$\backslash$table$[[$Month$,$Demand,Month,Demand$],[$Jan$-20,120,$Jan$-21,118],[$Feb$-20,105,$Feb$-21,110],[$Mar$-20,97,$Mar$-21,95],[$Apr$-20,85,$Apr$-21,90],[$May$-20,98,$May$-21,100],[$Jun$-20,110,$Jun$-21,115],[$Jul$-20,125,$Jul$-21,122],[$Aug$-20,102,$Aug$-21,98],[$Sep$-20,92,$Sep$-21,88],[$Oct$-20,90,$Oct$-21,79],[$Nov$-20,100,$Nov$-21,95],[$Dec$-20,115,$Dec$-21,110]]$

$($a$)$ Plot the demand data and comment on the pattern. What should be the most appropriate method to forecast demand for $2022?$

$(6$ marks$)$

$($b$)$ The supply chain manager believes there is a linear relationship between demand and time and decides to use a regression analysis method to forecast the demand. Determine the regression equation for the given data. Clearly identify the dependent variable, independent variable, slope and intercept. Discuss whether regression analysis is appropriate or not to forecast demand in this situation. Provide your reasons.

$(12$ marks$)$

$($c$)$ The actual demand for the months of Jan$-22$ to Apr$-22$ were found to be $120,100,80$ and $75,$ respectively. Compute the mean absolute deviation $($MAD$)$ based on the demand forecasts for $2022$ using the method in part $($b$).$

$(12$ marks$)$