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$(000)$

$4$

$6$

$4$

$5$

$10$

$8$

$7$

$9$

$12$

$14$

$15$

Part $2$

Use exponential smoothing with a smoothing constant of $0\mathrm{.}3$ to forecast the registrations at the seminar for years $2$ through $12.$ To begin the$$ procedure, assume that the forecast for year $1$ was $5$ comma $000$ people signing up $($round your responses to one decimal$$ place$)$:

Year

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

Forecast$(000)$

$5$

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Part $3$

$$a$)$ What is the$$ MAD?

Mean absolute deviation based on the forecast developed using the exponential smoothing method$($with a smoothing constant $($alpha$)$equals$0\mathrm{.}3$ and a starting forecast of Upper F $1$equals$5)$ is

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Part $4$

$$b$)$ What is the$$ MSE?

The mean squared error based on the forecast developed using the exponential smoothing method$($with a smoothing constant $($alpha$)$equals$0\mathrm{.}3$ and a starting forecast of Upper F $1$equals$5)$ is

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