Consider the following time series data.

a$.$ Construct a time series plot. What type of pattern exists in the data?

b$.$ Develop a three$-$week moving average for this time series. Compute MSE and a fore$-$

cast for week $8.$

c$.$ Use $=0\mathrm{.}2$ to compute the exponential smoothing values for the time series. Com$-$

pute MSE and a forecast for week $8.$

d$.$ Compare the three$-$week moving average forecast with the exponential smoothing

forecast using $=0\mathrm{.}2.$ Which appears to provide the better forecast based on MSE?

e$.$ Use trial and error to find a value of the exponential smoothing coefficient $$ that

results in a smaller MSE than what you calculated for $=0\mathrm{.}2.$