Chapter $4,$ Question $17($Note: Solved Problem $4\mathrm{.}1$ mentioned in the question can be found on page $138)$

Refer to Solved Problem $4\mathrm{.}1$ on page $144.$ Using smoothing constants of $\mathrm{.}6$ and $\mathrm{.}9,$ develop forecasts for the sales of VW Beetles. What effect did the smoothing constant have on the forecast? Use MAD to determine which of the three smoothing constants $(\mathrm{.}3,\mathrm{.}6,$ or $\mathrm{.}9)$ gives the most accurate forecast.

SOLVED PROBLEM $4\mathrm{.}1$

Sales of Volkswagen$$s popular Beetle have grown steadily at auto dealerships in Nevada during the past $5$ years $($see table below$).$ The sales manager had predicted before the new model was introduced that first year sales would be $410$ VWs$.$ Using exponential smoothing with a weight of a $5\mathrm{.}30,$ develop forecasts for years $2$ through $6.$

YEAR SALES FORECAST

$1450410$

$2495$

$3518$

$4563$

$5584$

$6?$

SOLUTION

YEAR FORECAST

$1410\mathrm{.}0$

$2422\mathrm{.}0=410+\mathrm{.}3(450-410)$

$3443\mathrm{.}9=422+\mathrm{.}3(495-422)$

$4466\mathrm{.}1=443\mathrm{.}9+\mathrm{.}3(518-443\mathrm{.}9)$

$5495\mathrm{.}2=466\mathrm{.}1+\mathrm{.}3(563-466\mathrm{.}1)$

$6521\mathrm{.}8=495\mathrm{.}2+\mathrm{.}3(584-495\mathrm{.}2)$

Group of answer choices