HW17

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Trine University *

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6933

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Statistics

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Feb 20, 2024

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docx

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Q1 Click on the datafile logo to reference the data. DATA I Quarter Year 1 Year 2 Year 3 1 1,690 1,800 1,850 2 940 900 1,100 3 2,625 2,900 2,930 - 2,500 2,360 2,615 a. Construct a time series plot. 1. Time Series Value r3000 -2500 -2000 r1500 r1000 -S00 2 4 9 8 10 12 Period

series plot 1 v/ @ What type of pattern exists in the data? | tinear trend and a seasonal pattern @ b. Show the four-quarter and centered moving average values for this time series (to 3 decimals if necessary). Time Series Four-Quarter Moving Centered Moving Year Quarter Value Average Average 1 ok 1690 2 940 1938.7 @ 3 2028 1952.5 @ 1966.2 @ 4 4800 1961.2 @ 1956.2 @ 2 1 1800 1990.6 @ 205 & 2 00 2007.5 & 1900 & 3 2900 10062 & 2: A Re6 20275 @

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The largest seasonal index is in thel third v/ @ quarter. Does this result appear reasonable? ‘ Yes Vl @ e. Deseasonalize the time series (to 3 decimals). Deseasonalized Year Quarter Value 1 1 1877.778 @ 2 1934.156 & 3 1879.026 & 4 2054232 & 2 1 2000.000 @ 2 1851.852 & 3 2075.877 & 4 1939.195 & 3 1 2055.556 @ 2 2263.372 & 3 2097.351 & 4 2148.726 & f. Compute the linear trend equation for the deseasonalized data (to 1 decimal if necessary). Let Period = 1 denote the time series value in Year 1 — Quarter 1; Period = 2 denote the time series value in Year 1 — Quarter 2; and so on. — Deseasonalized Value= 1851.6 @ + 25.1 @ Period Compute the forecast sales using the linear trend equation (to 1 decimal). Forecast for quarter 1 2178.6 @ Forecast for quarter 2 2203.8 @ Forecast for quarter 3 2228.9 @ Forecast for quarter 4 2254.1 @ g. Adjust the linear trend forecasts using the adjusted seasonal indexes computed in part (c) (to the nearest whole number). Forecast for quarter 1 1961 @ Forecast for quarter 2 1071 @ Forecast for quarter 3 3112 @ Forecast for quarter 4 2743 @ Q2

United Dairies, Inc., supplies milk to several independent grocers throughout Dade County, Florida. Managers at United Dairies want to develop a forecast of the number of half-gallons of milk sold per week. Sales data for the past 12 weeks follow. Click on the datafile logo to reference the data. pATA R Week Sales Week Sales 1 2,750 7 3,300 2 3,100 8 3,100 3 3,250 9 2,950 4 2,800 10 3,000 5 2,900 11 3,200 6 3,050 12 3,150 a. Which of the following time series plots is correct for this data? 2. Sales Volume 3400 3200 -3000 2800 2600 2400 2200 ‘v time series plot 2 v‘ @ What type of pattern exists in the data? l. horizontal v | @ b. Use exponential smoothing with & = 0.4 to develop a forecast of demand for week 13 (to the nearest whole number). 3117 0 half-gallons of milk

Consider the following time series. t | 1 2 3 B 5 6 7 Y; |120 110 100 96 94 92 88 Excel File: data17-19.xls a. Construct a time series plot. Time Series Value -140 1.2 3 4 5 ¢ Time Period (1, Time Series Value -140 120 r100 ‘. time series plot #2 V’ @ What type of pattern exists in the data? ‘. linear trend V” @ b. Develop the linear trend equation for this time series (to 1 decimal). T, = 119.7 @ + -4.9 @t c. What is the forecast for t = 8 (to 1 decimal)? 80.3 @ 5. The following data show the number of Netflix subscribers worldwide for the years 2012 (period 1) to 2017 (period 6) (datawrapper website). The data are in the file NetflixSubscribers. Click on the datafile logo to reference the data. DATA i Year Period Subscribers (millions) 2012 1 33.27 2013 2 44.35 2014 3 57.39 2015 4 74.76 2016 5 93.80 2017 6 117.58 a. Choose the correct time series plot.

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Subscribers ($ millions) +140 r120 r100 1 B 3 4 2 s Period ‘ Graph C V‘ @ What type of pattern exists in the data? |v Upward V‘ @ b. Develop a linear trend equation for this time series (to 4 decimals). y= 16.779 @ T+ 11.464 @ c. Develop a quadratic trend equation for this time series (to 4 decimals). Yy = 1.5625 @ z? + 5.8416 @ T + 26.048 @ d. Compare the MSE for each model (to 2 decimals). Linear model 15.30 @ Quadratic model 0.11 @ Which model appears better according to MSE? |. Quadratic model v| @ e. Use the models developed in parts (b) and (c) to forecast subscribers for 2018 (to 1 decimal). Linear model $ 128.9 @ million Quadratic model $ 143.5 @ million f. Which of the two forecasts in part (e) would you use? Explain. For the forecast one period ahead, the 1 quadratic v\ @ model is likely slightly preferred because of its | lower v‘@ MSE. 6.

Consider the following gasoline sales time series data. Click on the datafile logo to reference the data. DATA IR Week Sales (1000s of gallons) 1 17 21 19 23 18 16 20 18 22 20 15 12 22 O W N O A W N - = O a. Compute four-week and five-week moving averages for the time series (to 2 decimals). Time Series 4-Week Moving 5-Week Moving Week Value Average Forecast (Error)?2 Average Forecast (Error)? 1 17@ 2 21@ 3 19 & 4 1 5 18 & 2000 & 200 & 6 16 & 2025 & 18.06 & 19.60 & 12.06 & 7 20 & 19.00 & 1.00 & 19.40 & 036 & 8 18 & 1925 & 156 & 19.20 & 142 & 9 2 @ 18.00 & 16.00 & 19.00 & 9.00 & 10 20 & 19.00 & 1.00 & 18.80 & 144 & 11 15 & 2000 & 25.00 & 19.20 & 17.64 & 12 2 ¥ 18.75 & 1056 & 19.00 & 9.00 & Totals | 77.19| & s1.84 & b. Compute the MSE for the four-week and five-week moving average forecasts (to 2 decimals). MSE (4-Week) 9.65 & MSE (5-Week) 7.41 @ c. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 10.22. TheI 5-week v| @ moving average provides the smallest MSE. 7.

Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52, 7.52, 7.70, 7.62, and 7.55. a. Construct a time series plot. Index 7.9 7.8 7.7 7.6 7.5 7.4 7.3 7.2 7.1 3 3 4 2 ] 7 -] 9 10 Week What type of pattern exists in the data? [ horizontal v @ b. Compute the exponential smoothing forecasts for & = 0.2. Round your Time-series values and Forecast values to two decimal places and (Error)? values to four decimal places. Week Time-Series Value a = 0.2 Forecast (Error)? 1 7.35 @ 2 7.40 @ 7.35 @ 0.0025 @ 3 7.55 @ 7.36 @ 0.0361 @ 4 7.56 @ 7.40 @ 0.0262 @ 5 7.60 @ 7.43 @ 0.0288 @ 6 7.52 @ 7.46 @ 0.0031 @ 7 7.52 @ 7.48 @ 0.0020 @ 8 7.70 @ 7.48 @ 0.0465 @ 9 7.62 @ 7.53 @ 0.0086 @ 10 7.55 @ 7.55 @ 0.0000 @ Total 0.1538 @ c. Compute the exponential smoothing forecasts for & = 0.3. Round your Time-series values and Forecast values to two decimal places and (Error)? values to four Aarimal nlarac rovar R c. Compute the exponential smoothing forecasts for & = 0.3. Round your Time-series values and Forecast values to two decimal places and (Error)? values to four decimal places. Week Time-Series Value a = 0.3 Forecast (Error)2 1 7.35 @ 2 7.40 @ 735 @ o005 & 3 755 @ 737/ @ 0.03a2 @ 4 7.56 @ 742 @ 0.0105 & ??? 5 7.60 @ 7.46 @ 0.0189 @ 6 752 @ 7.50 @ 0.0003 @ 7 752 @ 751 @ 0.0001 & 8 7.70 @ 7.51 @ 0.0353 @ 9 7.62 @ 7.57 @ 0.0027 @ 10 755 @ 758 @ 0.0011 & Total 01147 & d. Which exponential smoothing constant provides more accurate forecasts based on MSE (to 4 decimals)? MSE (a = 0.2) 0.0171 @ MSE (@ = 0.3) 0.0127 @ Forecast week 11 (to 2 decimals). 7.57 @

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8. 9. For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. a. Construct a time series plot. 3 Monthly Percentage r87 86 r85 r84 83 F79 +78 12 3 4 5 6 7 8§ 9 1p 11 12 13 Month ‘ time series plot 3 v) @ What type of pattern exists in the data? ‘ horizontal v ' @ b. Compare the three-month moving average approach with the exponential smoothing approach for & = 0.2 (to 2 decimals). Round intermediate calculations to 2 decimal places. MSE (3-Month) 1.24 @ MSE (a = 0.2) 3.56 & Which provides more accurate forecasts using MSE as the measure of forecast accuracy? | A 3-month moving average v| @ provides the most accurate forecast using MSE. Which provides more accurate forecasts using MSE as the measure of forecast accuracy? \‘ A 3-month moving average v @ provides the most accurate forecast using MSE. c. What is the forecast for next month (to 1 decimal)? 83.3 @ 10.

Consider the following gasoline time series data. Click on the webfile logo to reference the data. DATA Week Sales (1000s of gallons) 1 17 21 19 23 18 16 20 18 22 20 15 12 22 O 0 N O U1 A W N L = O a. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of & = 0.1 or a = 0.2 for the gasoline sales time series? Calculate the MSE for each smoothing constant (to 2 decimals). MSE for a = 0.1 9.65 @ MSE for o« = 0.2 8.98 @ 'a=0.2 v| @ would be preferred based upon MSE. b. Are the results the same if you apply MAE as the measure of accuracy? Calculate the MAE (in 1000s of gallons) for each smoothing constant (to 2 decimals). MAE for o = 0.1 2.57 @ MAE for ¢ = 0.2 2.59 @ 'a=0.1 v @ would be preferred based upon MAE. c. What are the results if MAPE is used (to 2 decimals)? MAPE for a = 0.1 12.95 @ % MAPE for a = (.2 13.40 @ % ! a=0.1 v @ would be preferred based upon MAPE. 11.