a$.$

The data appear to follow a horizontal pattern.

b$.$ Three$-$week moving average

MSE $110427\mathrm{.}5.$

The forecast for week $8$ is F$8($Y$5$ Y$6$ Y$7)3$

$(192315)319.$

c$.$ Smoothing constant $0\mathrm{.}2$

Time Squared

Series Forecast Forecast

Week Value Forecast Error Error

$124$

$213$

$320$

$41219\mathrm{.}007\mathrm{.}0049\mathrm{.}00$

$51915\mathrm{.}004\mathrm{.}0016\mathrm{.}00$

$62317\mathrm{.}006\mathrm{.}0036\mathrm{.}00$

$71518\mathrm{.}003\mathrm{.}009\mathrm{.}00$

Total $110\mathrm{.}00$

$21$

$0$

$5$

$10$

$15$

$20$

$25$

Time Series Value

$30$

$34$

Week $($t$)$

$567$

Time Squared

Series Forecast Forecast

Week Value Forecast Error Error

$118$

$213185\mathrm{.}0025\mathrm{.}00$

$31616\mathrm{.}160\mathrm{.}160\mathrm{.}03$

$41116\mathrm{.}105\mathrm{.}1026\mathrm{.}03$

$51714\mathrm{.}232\mathrm{.}777\mathrm{.}69$

$61415\mathrm{.}251\mathrm{.}251\mathrm{.}55$

Total $60\mathrm{.}30$

Time Squared

Series Forecast Forecast

Week Value Forecast Error Error

$124$

$21324\mathrm{.}0011\mathrm{.}00121\mathrm{.}00$

$32021\mathrm{.}801\mathrm{.}803\mathrm{.}24$

$41221\mathrm{.}449\mathrm{.}4489\mathrm{.}11$

$51919\mathrm{.}550\mathrm{.}550\mathrm{.}30$

$62319\mathrm{.}443\mathrm{.}5612\mathrm{.}66$

$71520\mathrm{.}155\mathrm{.}1526\mathrm{.}56$

Total $252\mathrm{.}87$