Toyota Motors introduced a hybrid car Hybrid G in the U$.$S$.$ market in $2014.$ In the first three

years, the sales of the Hybrid G were strong, but the sales figures started to decline in $2017$

following the introduction of a new hybrid model by Honda. Toyota is in critical need of a better

forecasting method. They need your help to evaluate possible forecasting methods and provide

suggestions. The following table contains the past $12$ months of sales data.

Month Sales

$11,243$

$21,358$

$31,342$

$41,298$

$51,277$

$61,183$

$71,053$

$8992$

$9852$

$10910$

$11823$

$12744$

a$.$ Compute two forecasts for sales of Hybrid G for months $2$ to $13.(6$ points$)$

$$ A single exponential smoothing forecast with $=0\mathrm{.}7.$ Assume the forecast for

Month $1$ is $1,243.$

$$ A double exponential smoothing forecast with $=0\mathrm{.}8$ and $=0\mathrm{.}5.$ Assume that

for Month $1$ S$=1,243$ and T$=0.$

b$.$ Calculate the Mean Absolute Deviation $($MAD$)$ and the Mean Absolute Percent Error

$($MAPE$)$ for both forecasts for months $3$ to $12.(4$ points$)$

c$.$ Which forecast seems the most appropriate? Please explain why.