5. The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows: a) Using a 2-year moving average, the forecast for year 6 = Year Mileage 1 3,000 2 3,950 3 3,450 4 3,850 5 3,750 miles (round your response to the nearest whole number). b) If a 2-year moving average is used to make the forecast, the MAD based on this = miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) miles (round your response to the nearest whole number). c) The forecast for year 6 using a weighted 2-year moving average with weights of 0.40 and 0.60 (the weight of 0.60 is for the most recent period): The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.40 and 0.60 = d) Using exponential smoothing with a = 0.50 and the forecast for year 1 being 3,000, the forecast for year 6 = 6. Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the chip during the last 12 months were as follows: Month January February Price Per Chip $1.80 $1.61 = miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) miles (round your response to the nearest whole number). Month July August Price Per Chip $1.80 $1.70 PTET March April May June $1.60 $1.85 $1.88 $1.89 September October November December $1.65 $1.60 $1.50 $1.75 This exercise contains only parts a, b, and c. a) Using a 2-month moving average, the forecast for periods 11 and 12 is (round your responses to two decimal places): Mar Apr May Jun Forecast $1.71 1.61 1.73 1.87 Month Jul 1.89 Aug 1.85 Sep Oct Nov Dec 1.75 1.68 b) Using a 3-month moving average, the forecast for periods 11 and 12 is (round your responses to two decimal places): Apr May Jun Forecast $1.67 1.69 1.78 Month Jul 1.87 Aug 1.86 Sep Oct 1.80 1.72 Nov Dec c) The mean absolute deviation based on a 2-month moving average of March through December is $ The mean absolute deviation based on a 3-month moving average of April through December is $ (round your response to three decimal places). (round your response to three decimal places). 7. Registration numbers for an accounting seminar over the past 10 weeks are shown below: Week 0 0 1 C 7 0 10 7. Registration numbers for an accounting seminar over the past 10 weeks are shown below: Week Registrations 1 24 2 3 4 5 6 7 8 9 10 23 26 27 37 30 34 38 42 38 a) Starting with week 2 and ending with week 11, forecast registrations using the naive forecasting method (enter your responses as whole numbers). Week Forecast 1 2 3 4 5 6 7 8 9 10 11 24 23 26 27 37 30 34 38 b) Starting with week 3 and ending with week 11, forecast registration using a 2-week moving average (enter your responses as whole numbers). Week 1 2 3 4 5 6 7 8 9 10 11 Forecast - 23.5 24.5 26.5 32 33.5 32 36 c) Starting with week 5 and ending with week 11, forecast registrations using a 4-week moving average (enter your responses as whole numbers). Week 1 2 3 4 5 6 7 8 9 10 11 Forecast 25 28.25 30 32 34.75 d) Plot the original data and the three forecasts on the same graph. Choose the correct graph below. A. 45- 35- Registrations 25- Original data Naive 15- 4-week moving 2-week moving 1 Week 11 C. 45- Registrations 35- 25- . Registrations 45- 35- 25- 15- Original data Naive 2-week moving 4-week moving Week D. Registrations 45- 35- 25- 11 aper size Letter d) Plot the original data and the three forecasts on the same graph. Choose the correct graph below. A. Registrations 45- 35- 25 15- Original data Naive 4-week moving 2-week moving 11 1 Week C. Registrations 45- 35- 25- 15- Original data Naive 2-week moving 4-week moving Week 11 . Registrations 45- 35- 25- 15- D. Original data Naive 2-week moving 4-week moving 11 Week Registrations 45- 35- 25- Naive Original data 15- 2-week moving 4-week moving 11 The mean absolute deviations using the naive, 2- and 4-week moving average forecasting methods are 4.22, 4.00, and 5.50, respectively. Based on the MAD, the (1) has performed better. The mean squared errors using the naive, 2- and 4-week moving average forecasting methods are 24.9, 25.4, and 42.6, respectively. Based on the MSE, the (2) 2-week moving average forecast has performed better. (1) 4-week moving average forecast 2-week moving average forecast naive forecast naive forecast 4-week moving average forecast 8. Given the following data, use exponential smoothing (a = 0.15) to develop a demand forecast. Assume the forecast for the initial period is 6. Week Paper size Letter Print 8. Given the following data, use exponential smoothing (a = 0.15) to develop a demand forecast. Assume the forecast for the initial period is 6. Period Demand 1 2 3 4 5 6 9 10 9 11 12 9 The exponential smoothing forecast is (round your responses to two decimal places): Period Forecast 1 2 3 4 5 6 7 6.00 9. Consider the following actual and forecast demand levels for Big Mac hamburgers at a local McDonald's restaurant: Day Actual Demand Forecast Demand Monday 90.00 90.00 Tuesday Wednesday Thursday Friday 73.00 90.00 66.00 83.20 48.00 76.32 ? The forecast for Monday was derived by observing Monday's demand level and setting Monday's forecast level equal to this demand level. Subsequent forecasts were derived by using exponential smoothing with a smoothing constant of 0.40. Using this exponential smoothing method, the forecast for Big Mac demand for Friday is Big Macs (round your response to one decimal place). 10. Thamer Almutairi, owner of Almutairi's Department Store, has used time-series extrapolation to forecast retail sales for the next 4 quarters. The sales estimates are $110,000, $126,000, $142,000, and $158,000 for the respective quarters. Seasonal indices for the 4 quarters have been found to be 1.20, 0.90, 0.70, and 1.15, respectively. Compute a seasonalized or adjusted sales forecast for each quarter (enter your responses as whole numbers). Quarter || III IV EA EA EA Forecast 11. Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Gershon has collected the data shown in the following table: This exercise contains only parts b, c, and d. Maroon 5 TV Appearances Demand for Guitars b) Using the least-squares regression method, the equation for forecasting is (round your responses to four decimal places): Y = + 3 4 7 5 7 5 4 5 8 5 11 8 X c) The estimate for guitar sales if Maroon 5 performed on TV 10 times = sales (round your response to two decimal places). d) The correlation coefficient (r) for this model = (round your response to four decimal places). The coefficient of determination () for this model = (round your response to four decimal places). The percentage of variation in sales that can be explained by TV appearances = % (round your response to two decimal places). 12. The following data relate the sales figures of the bar in Mark Kaltenbach's small bed-and-breakfast inn in Portland, to the number of guests registered that week: Week Guests Bar Sales 1 16 $340 2 12 $265 3 4 18 14 $380 $300 a) The simple linear regression equation that relates bar sales to number of guests (not to time) is (round your responses to one decimal place): Bar Sales = + guests b) If the forecast is 24 guests next week, the bar sales are expected to be $ 1: Definition Determine the slope and intercept for the best-fit trend line. (round your response to one decimal place). 13. Emergency calls to the 911 system of Durham, North Carolina, for the past 24 weeks are shown in the table below. Assume a starting forecast of 51.00 for week 1 and an initial trend of zero. Using smoothing constants = 0.35 and = 0.20, the forecasts for weeks 2 through 20 have been developed and are provided below. Continuing with the given information, the forecast (Smoothed (F+) and Including Trend (FIT+)) and Trend Estimate (T+) for weeks 21 through 25 are (round your responses to two decimal places): Forecast Including Week Calls Smoothed Value (Ft) Trend Estimate Trend (T) (FIT) 1 51 51.00 0.00 51.00 8 234567 % O D 9 10 11 12 13 14 15 16 17 56 18 39 19 20 21 22 23 41 24 25 TOG NOG WONG SANWN TWAINW 34 51.00 0.00 51.00 25 45.05 - 1.19 43.86 40 37.26 -2.51 34.75 45 36.59 -2.14 34.45 36 38.14 - 1.40 36.74 19 36.48 - 1.45 35.03 29 29.42 -2.57 26.85 34 27.60 - 2.42 25.18 20 28.27 - 1.80 26.47 15 24.21 -2.25 21.96 40 19.52 - 2.74 16.78 54 24.91 -1.11 23.80 35 34.37 1.00 35.37 24 35.24 0.97 36.21 55 31.94 0.12 32.06 40.09 1.73 41.82 46.78 2.72 49.50 35 45.83 1.99 47.82 60 43.33 1.09 44.42 74 50 66