Develop a three$-$month moving average for this 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 $8$:

$($c$)$ Use $\backslash$alpha $=0\mathrm{.}2$ 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 $8$:

$($d$)$ Compare the three$-$month moving average forecast with the exponential smoothing forecast using $\backslash$alpha $=0\mathrm{.}2.$ Which appears to provide the better forecast based on MSE?

$-$ Select your answer $-$

$($e$)$ Use trial and error to find a value of the exponential smoothing coefficient $\backslash$alpha that results in the smallest MSE.

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

$\backslash$alpha $=$