If required, round your answers to two decimal places. Do not round intermediate calculation.

Month $1234567$

Value $23152012182215$

MSE:

The forecast for month $8$:

Use $=0\mathrm{.}2$ to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month $8.$

If required, round your answers to two decimal places. Do not round intermediate calculation.

MSE:

The forecast for month $8$:

Compare the three$-$month moving average forecast with the exponential smoothing forecast using $=0\mathrm{.}2.$ Which appears to provide the better forecast based on Ms

Use trial and error to find a value of the exponential smoothing coefficient a that results in the smallest MSE.

Do not round intermediate calculations. Use a two$-$decimal digit precision for the exponential smoothing coefficient.

$a=$