PLEASE SHOW ALL WORK AND INCLUDE FINAL ANSWERS

The manager of a small health clinic would like to use exponential smoothing to forecast demand for laboratory services in the facility.

However, she is not sure whether to use a high or low value of a$.$ To make her decision, she would like to compare the forecast accuracy

of a high and low $a$ on historical data. She has decided to use an $a=0\mathrm{.}7$ for the high value and $a=0\mathrm{.}1$ for the low value. Given the

following historical data, which do you think would be better to use? $($Round intermediate calculations to $4$ decimal places, e$.$g$.$

$15\mathrm{.}2516.$ Round answers to $2$ decimal place, e$.$g$.15\mathrm{.}25.)$

Forecasts using $a=0\mathrm{.}1,$MAD

Forecasts using $=0\mathrm{.}7,$MAD

Using $0\mathrm{.}1,$MAD or $0\mathrm{.}7,$MAD

provides a better historical fit based on the MAD criterion?