$$ BONUS QUESTION

Question:

The data below contains data on a motel chain's revenue and advertising.

a$.$ Use these data and multiple regression to make predictions of the motel chain's revenues during the next four quarters. Assume that advertising during each of the next four quarters is $$50,000.($Hint: Try using advertising, lagged by one period, as an explanatory variable. See the Problem $60$ for an explanation of a lagged variable. Also, use dummy variables for the quarters to account for possible seasonality.$)$

b$.$ Use simple exponential smoothing to make predictions for the motel chain's revenues during the next four quarters. Experiment with the smoothing constant.

c$.$ Use Holt's method to make forecasts for the motel chain's revenues during the next four quarters. Experiment with the smoothing constants.

d$.$ Use Winters' method to determine predictions for the motel chain's revenues during the next four quarters. Experiment with the smoothing constants.

e$.$ Which forecasts from parts a to d would you expect to be the most reliable?

Use Excel and provide formulas. Use MAPE $($mean absolute percentage error$)$ to evaluate the forecasting performance for each problem. Use the Palisade Decision Tools Excel software to complete these problems where requested and applicable.

Quarter

Advertising

Sales

$1$

$$30,000$

$$1,200,000$

$2$

$$20,000$

$$880,000$

$3$

$$15,000$

$$1,800,000$

$4$

$$40,000$

$$1,050,000$

$5$

$$10,000$

$$1,700,000$

$6$

$$50,000$

$$350,000$

$7$

$$5,000$

$$2,500,000$

$8$

$$40,000$

$$760,000$

$9$

$$20,000$

$$2,300,000$

$10$

$$10,000$

$$1,000,000$

$11$

$$60,000$

$$1,570,000$

$12$

$$5,000$

$$2,430,000$

$13$

$$35,000$

$$1,320,000$

$14$

$$15,000$

$$1,400,000$

$15$

$$70,000$

$$1,890,000$

$16$

$$25,000$

$$3,200,000$

$17$

$$30,000$

$$2,200,000$

$18$

$$60,000$

$$1,440,000$

$19$

$$80,000$

$$4,000,000$

$20$

$$50,000$

$$4,100,000$