Q$5(10$ points$)$

The purchasing$-$power value figures for the minimum wage $($in $$\text{'}$s$)$ for the years $1$ through $18$ are shown below:

a$)$ Use the above data and exponential smoothing to develop forecasts for the years $2$ through $18.$ Use $=0\mathrm{.}1,0\mathrm{.}5$ and $0\mathrm{.}8$ and

compare the results using Mean Absolute Deviation $($MAD$).$

b$)$ Select $$ which worked best and use your exponential smoothing results to the predict the minimum wage for year $19.$