Determine the following:

a$.$ The value of $$ consistent with $N=6$ in moving averages.

b$.$ The value of $N$ consistent with $=\mathrm{.}05.$

$c.$ The value of $$ that results in a variance of forecast error, ${}_e^2,10$ percent higher than the variance of each observation, ${}^2($refer to the formulas derived in Appendix $2-$A$).$

For the data for Problems $16$ through $21,$ use the arithmetic average of the first six months of data as a baseline to initialize the exponential smoothing.

a$.$ Determine the one$-$step$-$ahead exponential smoothing forecasts for August through December, assuming $=\mathrm{.}20.$

b$.$ Compare the accuracy of the forecasts obtained in part $($a$)$ with the one$-$stepahead six$-$month moving$-$average forecasts determined in Problem $20.$

c$.$ Comment on the reasons for the result you obtained in part $($b$).$