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Part $1$

Data collected on the yearly registrations for a Six Sigma seminar at the Quality College are shown in the following$$ table:

$$

Year

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

Registrations$(000)$

$3\mathrm{.}00$

$7\mathrm{.}00$

$5\mathrm{.}00$

$4\mathrm{.}00$

$9\mathrm{.}00$

$7\mathrm{.}00$

$6\mathrm{.}00$

$9\mathrm{.}00$

$11\mathrm{.}00$

$12\mathrm{.}00$

$12\mathrm{.}00$

Part $2$

$$a$)$ Calculate the forecasted registrations for years $2$ through $12$ using exponential$$ smoothing, with a smoothing constant $($alpha$)$ of $0\mathrm{.}30$ and a starting forecast of $4\mathrm{.}00$ for year $1($round your responses to one decimal $$place$)$:

Year

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

Forecast$(000)$

$4\mathrm{.}00$

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Part $3$

$$b$)$ Mean absolute deviation based on the forecast developed using the exponential smoothing method$($with a smoothing constant $($alpha$)=0\mathrm{.}30$ and a starting forecast of Upper F $1=4\mathrm{.}00)$ is

$$

enter your response here registrations $($round your response to one decimal$$ place$).$