The following shows the data on a motel chain's sales and advertising. If needed, round your predictions to the nearest thousand dollars, and the MAPE to one decimal digit.

a. Use these data and multiple regression to make predictions of the motel chain's sales 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 49 for an explanation of a lagged variable. Also, use dummy variables for the quarters to account for possible seasonality.)

Sales predictions for the next four quarters:

Sales $30,000 $1,200,000 20,000 $880,000 15,000 $1,800,000 $40,000 $1,050,000 $10,000 $1,700,000 $50,000 $350,000 $5,000 $2,500,000 $40,000 $760,000 $20,000 $2,300,000 $10,000 $1,000,000 $60,000 $1,570,000 $5,000 $2,430,000 35,000 $1,320,000 15,000 $1,400,000 $70,000 $1,890,000 $25,000 $3,200,000 $30,000 $2,200,000 $60,000 $1,440,000 $80,000 $4,000,000 $50,000 $4,100,000 Quarter Advertising 10 12 13 14 15 16 17 18 19 20 Sales predictions for the next four quarters: Quarter Q1 Q2 Q3 Q4 MAPE b. Use simple exponential smoothing to make predictions for the motel chain's sales during the next four quarters. Optimize the smoothing constant. Sales predictions for the next four quarters: Quarter Q1 Q2 Q3 Q4 MAPE Sales ($1,000) Sales ($1,000) c. Use Holt's method to make forecasts for the motel chain's sales during the next four quarters. Optimize the smoothing constants. Sales predictions for the next four quarters: Quarter Sales ($1,000) Q2 Q3 Q4 MAPE d. Use Winters' method to determine predictions for the motel chain's sales during the next four quarters Optimize the smoothing constants Sales predictions for the next four quarters: Quarter Sales ($1,000) Q2 Q3 Q4 MAPE e. Which forecasts from parts a to d would you expect to be the most reliable? The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Sales $30,000 $1,200,000 20,000 $880,000 15,000 $1,800,000 $40,000 $1,050,000 $10,000 $1,700,000 $50,000 $350,000 $5,000 $2,500,000 $40,000 $760,000 $20,000 $2,300,000 $10,000 $1,000,000 $60,000 $1,570,000 $5,000 $2,430,000 35,000 $1,320,000 15,000 $1,400,000 $70,000 $1,890,000 $25,000 $3,200,000 $30,000 $2,200,000 $60,000 $1,440,000 $80,000 $4,000,000 $50,000 $4,100,000 Quarter Advertising 10 12 13 14 15 16 17 18 19 20 Sales predictions for the next four quarters: Quarter Q1 Q2 Q3 Q4 MAPE b. Use simple exponential smoothing to make predictions for the motel chain's sales during the next four quarters. Optimize the smoothing constant. Sales predictions for the next four quarters: Quarter Q1 Q2 Q3 Q4 MAPE Sales ($1,000) Sales ($1,000) c. Use Holt's method to make forecasts for the motel chain's sales during the next four quarters. Optimize the smoothing constants. Sales predictions for the next four quarters: Quarter Sales ($1,000) Q2 Q3 Q4 MAPE d. Use Winters' method to determine predictions for the motel chain's sales during the next four quarters Optimize the smoothing constants Sales predictions for the next four quarters: Quarter Sales ($1,000) Q2 Q3 Q4 MAPE e. Which forecasts from parts a to d would you expect to be the most reliable? The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank