Information for Questions 1-2: The Instant paper Clip Company sells and delivers office supplies to various companies, schools, and agencies within a 30-mile radius of its warehouse. The office supply business is extremely competitive, and the ability to deliver orders promptly is an important factor in customer relations. The manager of the company wants to be certain that enough drivers and delivery vehicles are available so that orders can be delivered promptly. Therefore, the manager wants to be able to forecast the number of orders that will occur during the next month (i.e., to forecast the demand for deliveries). From records of delivery orders the manager has accumulated data for the past 10 months. These data are shown in the worksheets named MA and ES. The manager wants your help in fitting different models (Moving Average and Exponential Smoothing) to help forecast demand for deliveries. QUESTION 1: Moving Average Models -Worksheet MA (30 points) a. 2 Points: Using the Excel Insert Tab Line Graph and follow-up Chart Tools Tabs, construct an appropriate line chart displaying the time pattern of order deliveries. Please create a professional appearing chart with labeling and titles. A legend is probably not needed. Move the chart so that it starts in cell H4 and fits within the red shaded area. Is the time pattern stationary? Yes or No in cell K3. b. 2 Points: In column C (starting in the appropriate cell), write a formula using a built-in Excel function to forecast demand through October using an MA(3) model. c. 2 Points: In column D (starting in the appropriate cell), write a formula using a built-in Excel function to forecast demand through October using an MA(5) model. d. 2 Points: In cell B17, write a formula using a built-in Excel function to forecast demand for November using the MA(3) model you constructed. e. 2 Points: In cell B18, write a formula using a built-in Excel function to forecast demand for November using the MA(5) model you constructed. f. 3 Points: In column E, under the label \"MA(3) Error,\" write a formula in the appropriate cells calculating the error terms necessary to calculate the MAE for the MA(3) model. Do not construct a column of errors, then another column of absolute, squared, or absolute relative errors. Construct only one set of errors using the appropriate formula to make the errors absolute, squared, or absolute relative (whichever is appropriate for MAE). g. 2 Points: In column F, under the label \"MA(5) Error,\" write a formula in the appropriate cells calculating the error terms necessary to calculate the MAE for the MA(5) model. Do not construct a column of errors, then another column of absolute, squared, or absolute relative errors. Construct only one set of errors using the appropriate formula to make the errors absolute, squared, or absolute relative (whichever is appropriate for MAE). h. 2 Points: In cell B22, write a formula using a built-In Excel function referencing the appropriate cells to determine the MAE for the MA(3) model. i. 2 Points: In cell B23, write a formula using a built-In Excel function referencing the appropriate cells to determine the MAE for the MA(5) model. j. 2 Points: In cell B26, write the model that best fits the data according to the MAE calculations. That is, write either \"MA(3)\" or \"MA(5)\" in cell B26. k. 6 Points: Using StatTools replicate the MA(3) and MA(5) forecasting processes following the guidelines below: 1. Create the MA(3) forecast incorporating only Forecast Overlay and Forecast Errors Charts. Anchor the output in cell A1 of the StatToolsMA Worksheet. 2. Create the MA(5) forecast incorporating only Forecast Overlay and Forecast Errors Charts. Anchor the output in cell G1 of the StatToolsMA Worksheet. 3. Confirm that your StatTools results match the results you obtained in earlier segments of this Question. l. 3 points: Would your choice of model that best fits the data using MAE be the same if the criteria were MAPE? Place your answer (Yes or No) in cell I24. QUESTION 2: Exponential Smoothing Models -Worksheet ES (19 points) a. 3 Points: In column C (starting in the appropriate cell), write a formula to forecast demand through October using an ES model with smoothing constant alpha given in cell B1. Be sure to reference the cells containing the weights in the formula. b. 2 Points: In cell B20, write a formula to forecast demand for November using the ES model you constructed. c. 3 Points: In column D, under the label \"ES Error,\" write a formula in the appropriate cells calculating the error terms necessary to calculate the MAPE for the ES model. Do not construct a column of errors, then another column of absolute, squared, or absolute relative errors. Construct only one set of errors using the appropriate formula to make the errors absolute, squared, or absolute relative (whichever is appropriate for MAPE). d. 2 Points: In cell B24, write a formula using a built-In Excel function referencing the appropriate cells to determine the MAPE for the ES model. e. 6 Points: Using StatTools replicate the ES forecasting processes following the guidelines below: 1. Create the ES (alpha =0.2) forecast incorporating only Forecast Overlay and Forecast Errors Charts. Anchor the output in cell A1 of the StatToolsES Worksheet. 2. Follow the guidelines in our text to find the optimal alpha (smoothing constant) for the ES model of our data. Incorporate in you process only Forecast Overlay and Forecast Errors Charts. Anchor the output in cell G1 of the StatToolsES Worksheet. f. 3 Points: Which Metric does StatTools use for optimization? Place your answer in cell L29. What value does StatTools give as the optimal alpha? Place your answer in cell L30. What is the value of the MAPE at this alpha value? Place your answer in cell L31. Question 1 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Forecasts MA(3) = MA(5) = MAE MA(3) MA(5) Part Grader b c Orders MA(3) MA(5) Delivered Forecast Forecast 120 90 100 75 110 50 75 130 110 90 Value Value Part d e Grader Part h i Grader f g MA(3) Error MA(5) Error Part Grader Is the time pattern stationary? (Yes or No) StatTools MA(3) MA(5) Confirm Best? Best? Part j a Grader Part k.1. k.2. k.3. Part l Grader Grader alpha = Question 2 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Forecast = 0.20 Part a c Grader Orders ES Delivered Forecast ES Error 120 90 100 75 110 50 75 130 110 90 Value Part b Grader Value Part d Grader Part e.1. e.2. Grader Part f Grader MAPE StatTools ES(alpha=0.2) Optimal ES Metric alpha MAPE Question 3 Time 1 2 3 4 5 6 7 8 9 10 11 12 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec StatTools ES (Simple) ES (Holt's) Analysis Demand 37 40 41 37 45 50 43 47 56 52 55 54 Part b c d Grader ANALYSIS Part a Grader Is the time pattern stationary? (Yes or No) Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 Seasonally Adjusted Call Volume Part b Part a Day Mon Tue Wed Thur Fri Estimate for Seasonal Factor 3 3 3 3 4 4 4 4 4 5 5 5 5 5 Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 954 1,346 904 758 886 878 802 945 610 910 754 705 729 772 Part c Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 3 3 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 954 1,346 904 Seasonally Adjusted Call Volume Seasonally Adjusted Forecast MA(5) Final Forecast w/ Seasonal Factor 3 4 4 4 4 4 5 5 5 5 5 Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 758 886 878 802 945 610 910 754 705 729 772 Forecasting Error Mean Absolute Deviation MAD = Mean Square Error MSE = Estimate for Seasonal Factor Day Mon Tue Wed Thur Fri Part d Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 3 3 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 1,113 1,005 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 847 922 401 429 1,209 830 922 1,082 841 1,362 1,174 967 930 853 924 954 1,346 904 Seasonally Adjusted Call Volume Seasonally Adjusted Forecast Expo Smoothing 3 4 4 4 4 4 5 5 5 5 5 Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 55 56 57 58 59 60 61 62 63 64 65 758 886 878 802 945 610 910 754 705 729 772 Final Forecast w/ Seasonal Factor Forecasting Error alpha 0.9 Mean Absolute Deviation MAD = Mean Square Error MSE = Estimate for Seasonal Factor Day Mon Tue Wed Thur Fri Part e Parts f and g Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 3 3 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 954 1,346 904 Seasonally Adjusted Call Volume Seasonally Adjusted Forecast Your Model 3 4 4 4 4 4 5 5 5 5 5 Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 758 886 878 802 945 610 910 754 705 729 772 Final Forecast w/ Seasonal Factor Forecasting Error Mean Absolute Deviation MAD = Mean Square Error MSE = Estimate for Seasonal Factor Day Mon Tue Wed Thur Fri Describe your model here: Question 1 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Forecasts MA(3) = MA(5) = MAE MA(3) MA(5) Part Grader b c Orders MA(3) MA(5) Delivered Forecast Forecast 120 90 100 75 103 110 88 50 95 99 75 78 85 130 78 82 110 85 88 90 105 95 Value 110 91 Part d e Grader Value 27.14 26.80 Part h i Grader f g MA(3) Error MA(5) Error Part Grader Is the time pattern stationary? (Yes or No) Delivery Orders - Past 28 22 45 3 52 25 15 49 10 48 22 5 140 120 100 80 Number of Orders 60 40 20 0 Jan Feb Mar Apr StatTools MA(3) MA(5) Confirm Best? Best? MA(5) Part j a Grader No me pattern stationary? (Yes or No) No Delivery Orders - Past 10 Months 140 120 100 80 er of Orders 60 40 20 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Month Part k.1. k.2. k.3. Grader Part l Grader Moving Averages Forecasts for Orders Delivered MA(3) Forecasting Constant 3 Span Moving Averages 27.14 31.23 33.01% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 StatTools Student Version F or Academic Use Only 60.00 Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 StatTools Student Version F or Academic Use Only 0.00 -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 Forecast Error 103.33 88.33 95.00 78.33 78.33 85.00 105.00 110.00 -28.33 21.67 -45.00 -3.33 51.67 25.00 -15.00 Moving Averages Forecasts for Orders Delivered MA(5) Forecasting Constant 5 Span Moving Averages 26.80 32.60 34.76% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 tions sion Orders Delivered Forecast sion 08 May-2008 Jun-2008 Forecast Error 99.00 85.00 82.00 88.00 95.00 91.00 -49.00 -10.00 48.00 22.00 -5.00 alpha = 0.20 Question 2 Part Grader Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct a c Orders ES Delivered Forecast ES Error 120 90 120 30 100 114 14 75 111 36.2 110 104 6.04 50 105 55 75 94 19 130 90 40 110 98 12 90 101 11 Nov Forecast = Value 98 Part b Grader Part d Grader MAPE Value 24.7% Part e.1. e.2. Grader Part f Grader StatTools ES(alpha=0.2) Optimal ES Metric alpha MAPE Simple 0.2916224 30.88% Simple Exponential Smoothing Forecasts for Orders Delivered Forecasting Constant 0.200 Level (Alpha) Simple Exponential 24.73 29.21 32.21% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered Level 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 120.00 114.00 111.20 103.96 105.17 94.13 90.31 98.25 100.60 98.48 Forecast 120.00 114.00 111.20 103.96 105.17 94.13 90.31 98.25 100.60 98.48 Simple Exponential Smoothing Forecasts for Orders Delivered Forecasting Constant (Optimized) 0.292 Level (Alpha) Simple Exponential 24.43 28.93 30.88% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Error Forecasting Data Jan-2008 -30.00 -14.00 -36.20 6.04 -55.17 -19.13 39.69 11.75 -10.60 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 tions ion Orders Delivered Forecast ion ul-2008 Aug-2008 Sep-2008 Oct-2008 Level 120.00 111.25 107.97 98.36 101.75 86.66 83.26 96.89 100.71 97.59 Forecast Error 120.00 111.25 107.97 98.36 101.75 86.66 83.26 96.89 100.71 97.59 -30.00 -11.25 -32.97 11.64 -51.75 -11.66 46.74 13.11 -10.71 Question 3 Time 1 2 3 4 5 6 7 8 9 10 11 12 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec StatTools ES (Simple) ES (Holt's) Analysis Demand 37 40 41 37 45 50 43 47 56 52 55 54 Part b c d Grader ANALYSIS The optimal level/alpha for Simple Expo is .292 with a RMSE of 28.93. Holtz method optimal levelis .061 with a RMSE of 2 indicates the weghts decrease slower than the Simple with an alpha of .292. The higher the alpha, the faster the decrease introduces a beta at 0.000 which results in the trend line smoothing out. Referencing the forecast line graph trend lines for better because the trend line is smoother. The Holt ethod reacts quicker to sudden up or down swings whereas Simple Exp can forecast November orders of approx 85 at a RMSE of +/- 27.87. Part a Grader Is the time pattern stationary? (Yes or No) No Computer Demand - Past 12 Months 60 50 40 Demand 30 20 10 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month levelis .061 with a RMSE of 27.87. The alpha at .061, which is closer to zero, alpha, the faster the decrease in weights of past indicators. Hotz method cast line graph trend lines for both methods, one can see that the Holt method s wn swings whereas Simple Expo has delayed reactions to swings. With this, we Simple Exponential Smoothing Forecasts for Orders Delivered Forecasting Constant (Optimized) 0.292 Level (Alpha) Simple Exponential 24.43 28.93 30.88% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered Level 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 120.00 111.25 107.97 98.36 101.75 86.66 83.26 96.89 100.71 97.59 Forecast 120.00 111.25 107.97 98.36 101.75 86.66 83.26 96.89 100.71 97.59 Holt's Exponential Smoothing Forecasts for Orders Delivered Forecasting Constants (Optimized) 0.061 0.000 Level (Alpha) Trend (Beta) Holt's Exponential 23.48 27.87 30.19% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Error Forecasting Data -30.00 -11.25 -32.97 11.64 -51.75 -11.66 46.74 13.11 -10.71 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 tions ion Orders Delivered Forecast ion ul-2008 Aug-2008 Sep-2008 Oct-2008 ul-2008 Aug-2008 Sep-2008 Oct-2008 Level Trend Forecast Error 120.00 115.35 111.59 106.53 103.93 97.81 93.60 93.01 91.23 88.34 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 117.00 112.35 108.59 103.53 100.93 94.81 90.60 90.01 88.23 -27.00 -12.35 -33.59 6.47 -50.93 -19.81 39.40 19.99 1.77 85.34 Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 Seasonally Adjusted Call Volume 842.6874810549 752.1844506718 937.8325197479 974.5697062482 952.58944 809.1291300394 921.0061076381 973.8610100293 988.6939048895 1048.3732266667 971.700697181 990.8328662787 1095.0477500666 1310.0194239786 1318.6672 1977.7054865111 2496.9695336639 2009.9530487264 0 0 1453.4494695362 1332.0117122943 1079.7629360078 1165.2463879055 1422.3236266667 939.6338284329 1002.3233455486 1027.3578592349 996.9330207636 936.84416 747.2326159442 748.6489185888 1006.6141830123 991.0479379964 1028.6916266667 613.7449530161 0 0 471.9836379294 562.89376 901.6010306153 733.6229072358 0 1273.5319108219 1103.4817066667 1015.6994240679 1037.6786663793 1055.7439424869 1094.6253946991 1119.2269866667 689.0648075174 Part b Part a Day Mon Tue Wed Thur Fri Estimate for Seasonal Factor 1.3409478904 1.1313714332 0.9159417934 0.8496057231 0.7621331599 3 3 3 3 4 4 4 4 4 5 5 5 5 5 Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Average 954 1,346 904 758 886 878 802 945 610 910 754 705 729 772 946 843.2244018107 1469.5256945061 1064.0229643096 994.5768533333 660.7266444377 776.0492922325 875.6014910801 1112.2806430007 800.3850666667 678.624431646 666.4477976575 769.6995651016 858.0450674577 1012.9463466667 mae/mad Seasonal Consolidated Index Index deseasoned forecast re FC sq error error 1.194212 1.3409478904 842.68748105 0.899358 1.1313714332 752.18445067 0.907812 0.9159417934 937.83251975 0.875051 0.8496057231 974.56970625 0.767255 0.7621331599 952.58944 1.146655 1.3409478904 809.12913004 891.9727 1196.089 12340.75 1.101211 1.1313714332 921.00610764 885.261 1001.559 1635.469 0.942688 0.9159417934 973.86101003 919.0254 841.7738 2522.676 0.887733 0.8496057231 988.69390489 926.2311 786.9312 2816.295 0.844403 0.7621331599 1048.3732267 929.0559 708.0643 8269.297 1.377043 1.3409478904 971.70069718 948.2127 1271.504 992.0114 1.1847 1.1313714332 990.83286628 980.727 1109.566 130.7249 1.059995 0.9159417934 1095.0477501 994.6923 911.0803 8449.234 1.176246 0.8496057231 1310.019424 1018.93 865.6885 61162.98 1.062109 0.7621331599 1318.6672 1083.195 825.5387 32206.37 2.802699 1.3409478904 1977.7054865 1137.254 1524.998 1270134 2.98553 1.1313714332 2496.9695337 1338.455 1514.289 1717963 1.945614 0.9159417934 2009.9530487 1639.682 1501.853 115020.6 0 0.8496057231 0 1822.663 1548.545 2397991 0 0.7621331599 0 1560.659 1189.43 1414744 2.059751 1.3409478904 1453.4494695 1296.926 1739.11 44053.95 1.592635 1.1313714332 1332.0117123 1192.074 1348.679 25065.56 1.0452 0.9159417934 1079.762936 959.0828 878.4641 12218.19 1.046256 0.8496057231 1165.2463879 773.0448 656.7833 111033.4 1.145598 0.7621331599 1422.3236267 1006.094 766.7777 100630 1.331599 1.3409478904 939.63382843 1290.559 1730.572 221438.1 1.198439 1.1313714332 1002.3233455 1187.796 1343.838 44032.04 0.994472 0.9159417934 1027.3578592 1121.858 1027.557 7492.054 0.89513 0.8496057231 996.93302076 1111.377 944.2323 9454.114 0.754573 0.7621331599 936.84416 1077.714 821.3618 11526.56 1.058938 1.3409478904 747.23261594 980.6184 1314.958 97942.86 0.89513 1.1313714332 748.64891859 942.1382 1065.908 47920.82 0.974392 0.9159417934 1006.614183 891.4033 816.4736 11135.83 0.889846 0.8496057231 991.047938 887.2546 753.8166 7776.318 0.828551 0.7621331599 1028.6916267 886.0776 675.3091 11813.71 0.869767 1.3409478904 613.74495302 904.4471 1212.816 151956.8 0 1.1313714332 0 877.7495 993.0607 986169.6 0 0.9159417934 0 728.0197 666.8237 444653.9 0.423787 0.8496057231 471.98363793 526.6969 447.4847 2160.828 0.453378 0.7621331599 562.89376 422.884 322.294 11386.18 1.277701 1.3409478904 901.60103062 329.7245 442.1433 588069.1 0.877164 1.1313714332 733.62290724 387.2957 438.1753 153526.6 0 0.9159417934 0 534.0203 489.1315 239249.6 1.143484 0.8496057231 1273.5319108 534.0203 453.7067 394752.5 0.88879 0.7621331599 1103.4817067 694.3299 529.1719 97236.79 1.439395 1.3409478904 1015.6994241 802.4475 1076.04 81772.95 1.240712 1.1313714332 1037.6786664 825.2672 933.6837 57751.91 1.021949 0.9159417934 1055.7439425 886.0783 811.5962 24150.35 0.982847 0.8496057231 1094.6253947 1097.227 932.2104 4.886086 0.901471 0.7621331599 1119.2269867 1061.446 808.9631 1939.252 0.976506 1.3409478904 689.06480752 1064.595 1427.566 253579 200507.2 1.008211 1.1313714332 843.22440181 1.422486 0.9159417934 1469.5256945 0.955369 0.8496057231 1064.0229643 0.801073 0.7621331599 994.57685333 0.936347 1.3409478904 660.72664444 0.927892 1.1313714332 776.04929223 0.847573 0.9159417934 875.60149108 0.998699 0.8496057231 1112.280643 0.644663 0.7621331599 800.38506667 0.96171 1.3409478904 678.62443165 0.796846 1.1313714332 666.44779766 0.745061 0.9159417934 769.6995651 0.770425 0.8496057231 858.04506746 0.815869 0.7621331599 1012.9463467 999.268 960.3771 1043.133 1037.013 1012.083 1006.415 992.9803 874.1954 883.847 845.0086 848.5882 826.6679 805.4875 754.6404 797.1526 1130.543 879.6495 886.2522 790.342 1357.15 1138.63 909.5121 742.7215 673.6091 1133.113 960.0684 757.1797 684.3468 575.1365 0 31167.51 217482.8 314.986 1046.003 221982.8 67927.75 11558.86 40916.61 4046.117 49779.2 42464.2 2722.718 1993.909 38755.25 895352.7 Part c Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 Seasonally Adjusted Seasonally Adjusted Final Forecast Call Volume Forecast MA(5) w/ Seasonal Factor 842.6874810549 752.1844506718 937.8325197479 974.5697062482 952.58944 809.1291300394 891.9727195446 1,196 921.0061076381 885.2610493415 1,002 973.8610100293 919.0253807347 842 988.6939048895 926.231078791 787 1048.3732266667 929.0559185193 708 971.700697181 948.2126758526 1,272 990.8328662787 980.7269892809 1,110 1095.0477500666 994.692341009 911 1310.0194239786 1018.9296890165 866 1318.6672 1083.1947928343 826 1977.7054865111 2496.9695336639 2009.9530487264 0 0 1453.4494695362 1332.0117122943 1079.7629360078 1165.2463879055 1422.3236266667 939.6338284329 1002.3233455486 1027.3578592349 996.9330207636 936.84416 747.2326159442 748.6489185888 1006.6141830123 991.0479379964 1028.6916266667 613.7449530161 0 0 471.9836379294 562.89376 901.6010306153 733.6229072358 0 1273.5319108219 1103.4817066667 1137.253587501 1338.454545367 1639.681878844 1822.662938576 1560.6590537803 1296.9256137803 1192.0744103853 959.0828461114 773.0448235677 1006.0941011488 1290.5588264821 1187.7956982614 1121.8580249123 1111.3770095577 1077.7143361293 980.618442796 942.1382002983 891.4033149063 887.2545796618 886.0775631083 904.4470564417 877.749523856 728.0197401383 526.6969035358 422.8840435224 329.7244701891 387.2956857089 534.0202671561 534.0202671561 694.3299217346 1,525 1,514 1,502 1,549 1,189 1,739 1,349 878 657 767 1,731 1,344 1,028 944 821 1,315 1,066 816 754 675 1,213 993 667 447 322 442 438 489 454 529 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed 1,362 1,174 967 930 853 924 954 1,346 904 758 886 878 802 945 610 910 754 705 1015.6994240679 1037.6786663793 1055.7439424869 1094.6253946991 1119.2269866667 689.0648075174 843.2244018107 1469.5256945061 1064.0229643096 994.5768533333 660.7266444377 776.0492922325 875.6014910801 1112.2806430007 800.3850666667 678.624431646 666.4477976575 769.6995651016 802.4475110679 825.2671897585 886.0783415872 1097.2271300845 1061.44582686 1064.59488286 999.2679595499 960.3771066362 1043.13345704 1037.0129709621 1012.0829442955 1006.4153116795 992.9802897639 874.1954490787 883.8469848169 845.0086274835 848.5881849252 826.6678860102 1,076 934 812 932 809 1,428 1,131 880 886 790 1,357 1,139 910 743 674 1,133 960 757 5 5 Thur Fri Average 729 772 858.0450674577 1012.9463466667 805.4875008145 754.6403857059 684 575 946 Forecasting Error Error ^2 Mean Absolute Deviation MAD = 298.3432032893 Mean Square Error MSE = 111.09 40.44 50.23 53.07 90.94 31.50 11.43 91.92 247.31 179.46 12,340.75 1,635.47 2,522.68 2,816.29 8,269.30 992.01 130.72 8,449.23 61,162.98 32,206.37 1,127.00 1,310.71 339.15 1,548.54 1,189.43 209.89 158.32 110.54 333.22 317.22 470.57 209.84 86.56 97.23 107.36 312.96 218.91 105.53 88.18 108.69 389.82 993.06 666.82 46.48 106.71 766.86 391.82 489.13 628.29 311.83 1,270,133.96 1,717,962.70 115,020.58 2,397,991.20 1,414,743.76 44,053.95 25,065.56 12,218.19 111,033.36 100,630.00 221,438.14 44,032.04 7,492.05 9,454.11 11,526.56 97,942.86 47,920.82 11,135.83 7,776.32 11,813.71 151,956.80 986,169.63 444,653.86 2,160.83 11,386.18 588,069.15 153,526.62 239,249.61 394,752.50 97,236.79 447.78 Estimate for Seasonal Factor Day Mon Tue Wed Thur 1.3409478904 1.1313714332 0.9159417934 0.8496057231 Fri 0.7621331599 285.96 240.32 155.40 2.21 44.04 503.57 176.54 466.35 17.75 32.34 471.15 260.63 107.51 202.28 63.61 223.11 206.07 52.18 81,772.95 57,751.91 24,150.35 4.89 1,939.25 253,578.98 31,167.51 217,482.76 314.99 1,046.00 221,982.78 67,927.75 11,558.86 40,916.61 4,046.12 49,779.20 42,464.20 2,722.72 44.65 196.86 1,993.91 38,755.25 Moving Averages Forecasts for Call Volume Forecasting Constant Span 5 Moving Averages Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecasting Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 297.62 458.91 #NAME? Call Volume Forecast Error 891.97 885.26 919.03 926.23 929.06 948.21 980.73 994.69 1018.93 1083.19 1137.25 1338.45 1639.68 1822.66 1560.66 1296.93 1192.07 959.08 773.04 1006.09 1290.56 1187.80 1121.86 1111.38 1077.71 980.62 942.14 891.40 887.25 886.08 -82.84 35.75 54.84 62.46 119.32 23.49 10.11 100.36 291.09 235.47 840.45 1158.51 370.27 -1822.66 -1560.66 156.52 139.94 120.68 392.20 416.23 -350.92 -185.47 -94.50 -114.44 -140.87 -233.39 -193.49 115.21 103.79 142.61 842.69 752.18 937.83 974.57 952.59 809.13 921.01 973.86 988.69 1048.37 971.70 990.83 1095.05 1310.02 1318.67 1977.71 2496.97 2009.95 0.00 0.00 1453.45 1332.01 1079.76 1165.25 1422.32 939.63 1002.32 1027.36 996.93 936.84 747.23 748.65 1006.61 991.05 1028.69 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 613.74 0.00 0.00 471.98 562.89 901.60 733.62 0.00 1273.53 1103.48 1015.70 1037.68 1055.74 1094.63 1119.23 689.06 843.22 1469.53 904.45 877.75 728.02 526.70 422.88 329.72 387.30 534.02 534.02 694.33 802.45 825.27 886.08 1097.23 1061.45 1064.59 999.27 960.38 -290.70 -877.75 -728.02 -54.71 140.01 571.88 346.33 -534.02 739.51 409.15 213.25 212.41 169.67 -2.60 57.78 -375.53 -156.04 509.15 1064.02 994.58 660.73 776.05 875.60 1112.28 800.39 678.62 666.45 769.70 858.05 1012.95 1043.13 1037.01 1012.08 1006.42 992.98 874.20 883.85 845.01 848.59 826.67 805.49 754.64 797.15 20.89 -42.44 -351.36 -230.37 -117.38 238.09 -83.46 -166.38 -182.14 -56.97 52.56 258.31 Part d Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 Seasonally Adjusted Seasonally Adjusted Call Volume Forecast Expo Smoothing 842.6874810549 752.1844506718 842.6874810549 937.8325197479 761.2347537101 974.5697062482 920.1727431442 952.58944 969.1300099378 809.1291300394 954.2434969938 921.0061076381 823.6405667348 973.8610100293 911.2695535478 988.6939048895 967.6018643811 1048.3732266667 986.5847008387 971.700697181 1042.1943740839 990.8328662787 978.7500648713 1095.0477500666 989.6245861379 1310.0194239786 1084.5054336737 1318.6672 1287.4680249481 1977.7054865111 2496.9695336639 2009.9530487264 0 0 1453.4494695362 1332.0117122943 1079.7629360078 1165.2463879055 1422.3236266667 939.6338284329 1002.3233455486 1027.3578592349 996.9330207636 936.84416 747.2326159442 748.6489185888 1006.6141830123 991.0479379964 1028.6916266667 613.7449530161 0 0 471.9836379294 562.89376 901.6010306153 733.6229072358 0 1273.5319108219 1103.4817066667 1315.5472824948 1911.4896661094 2438.4215469084 2052.7998985446 205.2799898545 20.5279989854 1310.1573224812 1329.826273313 1104.7692697383 1159.1986760888 1396.0111316089 985.2715587505 1000.6181668688 1024.6838899983 999.708107687 943.1305547687 766.8224098267 750.4662677126 980.9993914824 990.043083345 1024.8267723345 654.8531349479 65.4853134948 6.5485313495 425.4401272714 549.1483967271 866.3557672265 746.8961932348 74.6896193235 1153.6476816721 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 1,362 1,174 967 930 853 924 954 1,346 904 758 886 878 802 945 610 910 754 705 1015.6994240679 1037.6786663793 1055.7439424869 1094.6253946991 1119.2269866667 689.0648075174 843.2244018107 1469.5256945061 1064.0229643096 994.5768533333 660.7266444377 776.0492922325 875.6014910801 1112.2806430007 800.3850666667 678.624431646 666.4477976575 769.6995651016 1108.4983041672 1024.9793120778 1036.4087309491 1053.8104213331 1090.5438973625 1116.3586777363 731.7941945393 832.0813810836 1405.7812631638 1098.1987941951 1004.9390474195 695.1478847359 767.9591514829 864.8372571204 1087.5363044127 829.1001904413 693.6720075255 669.1702186443 5 5 Thur Fri 64 65 Average = 729 772 858.0450674577 1012.9463466667 759.6466304559 848.2052237575 946 Final Forecast w/ Seasonal Factor Forecasting Error alpha 0.9 error^2 953.3925431949 697.2467254737 781.7840288269 738.6061168333 1279.5908042364 931.8434084423 834.669869102 822.080081672 751.9089155648 1397.5283473306 1107.3298636544 906.4385181705 921.4020231952 981.2220741312 102.392543195 161.753274526 46.2159711731 12.6061168333 194.590804236 110.156591558 57.330130898 17.919918328 47.0910844352 94.5283473306 13.6701363456 96.5614818295 191.597976805 23.7779258688 Mean Absolute Deviation 10484.232902 MAD = 255.3970949939 26164.12182 2135.9159915 Mean Square Error 158.91418162 MSE = 447.9561951673 37865.581093 12134.474664 3286.7439088 321.12347288 Estimate for 2217.5702333 Seasonal Factor 8935.608449 Day 186.87262771 Mon 1.3409478904 9324.1197731 Tue 1.1313714332 36709.784716 Wed 0.9159417934 565.38975862 Thur 0.8496057231 1764.0803532032 2162.6048031254 2233.4522046189 1744.0705422071 156.4506873332 27.526976934 1482.274567675 1218.0434616224 938.6182942879 883.463749966 1871.9781819274 1114.7080955313 916.5079982205 870.5772973232 761.9106990949 1264.6889278034 867.5609688284 687.3834190974 833.4626973727 754.5446635525 1374.2392984032 740.8821298325 59.9807354805 5.5636697125 324.242028548 736.3793841163 980.1701660427 684.1134386779 63.4567280343 879.2331530506 887.919646797 662.395196875 392.452204619 1744.07054221 156.450687333 1921.47302307 24.725432325 229.043461622 51.3817057121 200.536250034 611.978181927 19.2919044687 24.4920017795 23.5772973232 47.9106990949 262.688927803 20.5609688284 234.616580903 8.5373026273 29.4553364475 551.239298403 740.882129833 59.9807354805 395.436330288 104.757971452 472.620615884 150.170166043 684.113438678 1018.54327197 38.2331530506 788401.29917 438767.39684 154018.73291 3041782.0562 24476.817567 3692058.5784 611.34700366 52460.907312 2640.0796819 40214.787578 374517.29516 372.17757803 599.85815117 555.88894907 2295.4350878 69005.472791 422.75343916 55044.940034 72.885536149 867.61684524 303864.7641 548906.33031 3597.6886288 156369.89131 10974.232583 223370.24656 22551.078769 468011.19698 1037430.3969 1461.7739922 Fri 0.7621331599 1486.4384625021 1159.6323133231 949.2900716693 895.3233650396 831.1396665127 1496.9788138574 827.9310466957 762.138112403 1194.3598066275 836.9737172245 1347.5708956333 786.4704586513 703.4058824289 734.7706832099 828.8474801942 1111.7801513152 784.8006933365 612.9209701216 124.438462502 14.3676866769 17.7099283307 34.6766349604 21.8603334873 572.978813857 126.068953304 583.861887597 290.359806628 78.9737172245 461.570895633 91.5295413487 98.5941175711 210.22931679 218.847480194 201.780151315 30.8006933365 92.0790298784 15484.93095 206.43042045 313.64156148 1202.4690122 477.87418017 328304.72113 15893.380987 340894.70379 84308.817305 6236.8480123 213047.6917 8377.6569395 9720.8000196 44196.365638 47894.219587 40715.229465 948.68271001 8478.5477433 645.400124778 83.599875222 6988.9391371 720.6400124778 51.3599875222 2637.8483183 Simple Exponential Smoothing Forecasts for Call Volume Forecasting Constant Level (Alpha) 0.900 Simple Exponential Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecasting Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 248.17 432.07 #NAME? Call Volume Level Forecast 842.69 752.18 937.83 974.57 952.59 842.69 761.23 920.17 969.13 954.24 842.69 761.23 920.17 969.13 809.13 921.01 973.86 988.69 1048.37 971.70 990.83 1095.05 1310.02 1318.67 1977.71 2496.97 2009.95 0.00 0.00 1453.45 1332.01 1079.76 1165.25 1422.32 939.63 1002.32 1027.36 996.93 936.84 747.23 748.65 1006.61 991.05 1028.69 823.64 911.27 967.60 986.58 1042.19 978.75 989.62 1084.51 1287.47 1315.55 1911.49 2438.42 2052.80 205.28 20.53 1310.16 1329.83 1104.77 1159.20 1396.01 985.27 1000.62 1024.68 999.71 943.13 766.82 750.47 981.00 990.04 1024.83 954.24 823.64 911.27 967.60 986.58 1042.19 978.75 989.62 1084.51 1287.47 1315.55 1911.49 2438.42 2052.80 205.28 20.53 1310.16 1329.83 1104.77 1159.20 1396.01 985.27 1000.62 1024.68 999.71 943.13 766.82 750.47 981.00 990.04 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 613.74 0.00 0.00 471.98 562.89 901.60 733.62 0.00 1273.53 1103.48 1015.70 1037.68 1055.74 1094.63 1119.23 689.06 843.22 1469.53 654.85 65.49 6.55 425.44 549.15 866.36 746.90 74.69 1153.65 1108.50 1024.98 1036.41 1053.81 1090.54 1116.36 731.79 832.08 1405.78 1024.83 654.85 65.49 6.55 425.44 549.15 866.36 746.90 74.69 1153.65 1108.50 1024.98 1036.41 1053.81 1090.54 1116.36 731.79 832.08 1064.02 994.58 660.73 776.05 875.60 1112.28 800.39 678.62 666.45 769.70 858.05 1012.95 1098.20 1004.94 695.15 767.96 864.84 1087.54 829.10 693.67 669.17 759.65 848.21 996.47 1405.78 1098.20 1004.94 695.15 767.96 864.84 1087.54 829.10 693.67 669.17 759.65 848.21 996.47 Error -90.50 176.60 54.40 -16.54 -145.11 97.37 62.59 21.09 61.79 -70.49 12.08 105.42 225.51 31.20 662.16 585.48 -428.47 -2052.80 -205.28 1432.92 21.85 -250.06 60.48 263.12 -456.38 17.05 26.74 -27.75 -62.86 -195.90 -18.17 256.15 10.05 38.65 -411.08 -654.85 -65.49 465.44 137.45 352.45 -132.73 -746.90 1198.84 -50.17 -92.80 12.70 19.34 40.81 28.68 -427.29 111.43 637.44 -341.76 -103.62 -344.21 80.90 107.64 247.44 -287.15 -150.48 -27.22 100.53 98.40 164.74 Part e Simple Exponential Smoothing Forecasts for Call Volume Forecasting Constant (Optimized) Level (Alpha) 0.251 Simple Exponential Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecasting Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 272.68 422.73 #NAME? Call Volume Level Forecast 842.69 752.18 937.83 842.69 819.99 849.55 842.69 819.99 974.57 952.59 809.13 921.01 973.86 988.69 1048.37 971.70 990.83 1095.05 1310.02 1318.67 1977.71 2496.97 2009.95 0.00 0.00 1453.45 1332.01 1079.76 1165.25 1422.32 939.63 1002.32 1027.36 996.93 936.84 747.23 748.65 1006.61 880.90 898.88 876.37 887.57 909.21 929.15 959.05 962.22 969.40 1000.91 1078.44 1138.69 1349.13 1637.03 1730.56 1296.51 971.33 1092.25 1152.39 1134.17 1141.97 1212.28 1143.90 1108.39 1088.07 1065.21 1033.01 961.33 907.99 932.73 849.55 880.90 898.88 876.37 887.57 909.21 929.15 959.05 962.22 969.40 1000.91 1078.44 1138.69 1349.13 1637.03 1730.56 1296.51 971.33 1092.25 1152.39 1134.17 1141.97 1212.28 1143.90 1108.39 1088.07 1065.21 1033.01 961.33 907.99 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 991.05 1028.69 613.74 0.00 0.00 471.98 562.89 901.60 733.62 0.00 1273.53 1103.48 1015.70 1037.68 1055.74 1094.63 1119.23 689.06 947.35 967.75 878.96 658.51 493.34 487.99 506.77 605.80 637.86 477.88 677.44 784.30 842.34 891.33 932.57 973.21 1009.84 929.38 932.73 947.35 967.75 878.96 658.51 493.34 487.99 506.77 605.80 637.86 477.88 677.44 784.30 842.34 891.33 932.57 973.21 1009.84 843.22 1469.53 1064.02 994.58 660.73 776.05 875.60 1112.28 800.39 678.62 666.45 769.70 858.05 1012.95 907.77 1048.67 1052.52 1037.99 943.36 901.40 894.93 949.44 912.06 853.51 806.59 797.34 812.56 862.82 929.38 907.77 1048.67 1052.52 1037.99 943.36 901.40 894.93 949.44 912.06 853.51 806.59 797.34 812.56 862.82 Error -90.50 117.84 125.02 71.69 -89.75 44.63 86.29 79.48 119.23 12.65 28.61 125.65 309.11 240.23 839.01 1147.84 372.93 -1730.56 -1296.51 482.12 239.76 -72.62 31.08 280.36 -272.65 -141.58 -81.03 -91.13 -128.36 -285.78 -212.69 98.62 58.32 81.34 -354.01 -878.96 -658.51 -21.36 74.91 394.83 127.82 -637.86 795.66 426.04 231.40 195.34 164.41 162.06 146.01 -320.77 -86.16 561.75 15.35 -57.94 -377.26 -167.31 -25.80 217.35 -149.06 -233.43 -187.06 -36.89 60.71 200.38 Holt's Exponential Smoothing Forecasts for Call Volume Forecasting Constants (Optimized) Level (Alpha) Trend (Beta) 0.255 0.000 Holt's Exponential Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecasting Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 270.87 422.86 #NAME? Call Volume Level Trend 842.69 752.18 937.83 974.57 842.69 821.61 853.14 886.00 2.62 2.62 2.62 2.62 952.59 809.13 921.01 973.86 988.69 1048.37 971.70 990.83 1095.05 1310.02 1318.67 1977.71 2496.97 2009.95 0.00 0.00 1453.45 1332.01 1079.76 1165.25 1422.32 939.63 1002.32 1027.36 996.93 936.84 747.23 748.65 1006.61 991.05 904.90 882.48 894.24 916.45 936.79 967.15 970.26 977.45 1009.33 1087.81 1148.52 1361.52 1652.46 1745.40 1303.12 973.40 1097.54 1159.17 1140.91 1149.06 1220.56 1151.01 1115.12 1094.74 1071.80 1039.40 966.99 913.37 939.06 954.24 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 1028.69 613.74 0.00 0.00 471.98 562.89 901.60 733.62 0.00 1273.53 1103.48 1015.70 1037.68 1055.74 1094.63 1119.23 689.06 843.22 975.14 885.11 661.79 495.30 491.32 511.49 612.73 645.45 483.13 686.25 794.40 852.68 901.72 942.87 983.45 1019.96 937.69 915.60 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 1469.53 1064.02 994.58 660.73 776.05 875.60 1112.28 800.39 678.62 666.45 769.70 858.05 1012.95 1058.54 1061.89 1046.71 950.42 907.99 901.70 957.25 919.28 859.98 812.67 803.69 819.48 870.67 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 Forecast Error 845.31 824.22 855.76 -93.12 113.61 118.81 888.62 907.52 885.10 896.86 919.07 939.41 969.76 972.88 980.07 1011.95 1090.43 1151.14 1364.14 1655.08 1748.02 1305.74 976.02 1100.16 1161.79 1143.53 1151.68 1223.18 1153.63 1117.74 1097.36 1074.42 1042.02 969.61 915.99 941.68 63.97 -98.39 35.91 77.01 69.62 108.96 1.94 17.96 114.98 298.07 228.23 826.56 1132.83 354.87 -1748.02 -1305.74 477.43 231.86 -82.02 21.72 270.65 -283.55 -151.31 -90.38 -100.42 -137.57 -294.79 -220.96 90.62 49.37 956.86 977.76 887.73 664.41 497.92 493.94 514.11 615.35 648.07 485.75 688.87 797.02 855.30 904.33 945.49 986.07 1022.58 940.31 71.83 -364.02 -887.73 -664.41 -25.94 68.95 387.49 118.27 -648.07 787.79 414.61 218.68 182.38 151.41 149.13 133.16 -333.51 -97.09 918.22 1061.16 1064.51 1049.33 953.04 910.61 904.32 959.87 921.90 862.60 815.29 806.31 822.10 873.29 551.30 2.87 -69.93 -388.60 -176.99 -35.01 207.96 -159.48 -243.27 -196.15 -45.59 51.74 190.85 Parts f and g Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 3 3 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 954 1,346 904 Seasonally Adjusted Call Volume 842.6874810549 752.1844506718 937.8325197479 974.5697062482 952.58944 809.1291300394 921.0061076381 973.8610100293 988.6939048895 1048.3732266667 971.700697181 990.8328662787 1095.0477500666 1310.0194239786 1318.6672 1977.7054865111 2496.9695336639 2009.9530487264 0 0 1453.4494695362 1332.0117122943 1079.7629360078 1165.2463879055 1422.3236266667 939.6338284329 1002.3233455486 1027.3578592349 996.9330207636 936.84416 747.2326159442 748.6489185888 1006.6141830123 991.0479379964 1028.6916266667 613.7449530161 0 0 471.9836379294 562.89376 901.6010306153 733.6229072358 0 1273.5319108219 1103.4817066667 1015.6994240679 1037.6786663793 1055.7439424869 1094.6253946991 1119.2269866667 689.0648075174 843.2244018107 1469.5256945061 1064.0229643096 Seasonal Adj MA5 Seasonally Adjusted Forecast Your Model 891.9727195446 885.2610493415 919.0253807347 926.231078791 929.0559185193 948.2126758526 980.7269892809 994.692341009 1018.9296890165 1083.1947928343 1137.253587501 1338.454545367 1639.681878844 1822.662938576 1560.6590537803 1296.9256137803 1192.0744103853 959.0828461114 773.0448235677 1006.0941011488 1290.5588264821 1187.7956982614 1121.8580249123 1111.3770095577 1077.7143361293 980.618442796 942.1382002983 891.4033149063 887.2545796618 886.0775631083 904.4470564417 877.749523856 728.0197401383 526.6969035358 422.8840435224 329.7244701891 387.2956857089 534.0202671561 534.0202671561 694.3299217346 802.4475110679 825.2671897585 886.0783415872 1097.2271300845 1061.44582686 1064.59488286 999.2679595499 960.3771066362 1043.13345704 3 4 4 4 4 4 5 5 5 5 5 Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 758 886 878 802 945 610 910 754 705 729 772 994.5768533333 660.7266444377 776.0492922325 875.6014910801 1112.2806430007 800.3850666667 678.624431646 666.4477976575 769.6995651016 858.0450674577 1012.9463466667 1037.0129709621 1012.0829442955 1006.4153116795 992.9802897639 874.1954490787 883.8469848169 845.0086274835 848.5881849252 826.6678860102 805.4875008145 754.6403857059 873.2904768213 Final Forecast w/ Seasonal Factor 0 0 0 0 0 1196.0889365814 1001.5590621645 841.7737553645 786.931225465 708.0643229102 1271.5037873497 1109.5664994572 911.0802866554 865.6884952371 825.5386702562 1524.9977990268 1514.2892372874 1501.8531606321 1548.5448639182 1189.430016193 1739.1096658244 1348.6789341787 878.4640620386 656.7833063252 766.777676471 1730.5721358282 1343.8381215108 1027.5566512224 944.2322678553 821.3618324699 1314.9582321697 1065.9082459598 816.4735508535 753.8165687379 675.3090930933 1212.8163723279 993.0607368104 666.8237063766 447.4847035894 322.2939523634 442.1433327184 438.1752750192 489.1314811843 453.7066752336 529.1718572687 1076.0402971357 933.6837232638 811.596185242 932.2104492735 808.9630620935 1427.5662623181 1130.5432235636 879.6495293447 886.2521550707 Forecasting Error 111.0889365814 40.4409378355 50.2262446355 53.068774535 90.9356770898 31.4962126503 11.4335005428 91.9197133446 247.3115047629 179.4613297438 1127.002200973 1310.710762713 339.1468393679 1548.544863918 1189.430016193 209.8903341756 158.3210658213 110.5359379614 333.2166936748 317.222323529 470.5721358282 209.8381215108 86.5566512224 97.2322678553 107.3618324699 312.9582321697 218.9082459598 105.5264491465 88.1834312621 108.6909069067 389.8163723279 993.0607368104 666.8237063766 46.4847035894 106.7060476366 766.8566672816 391.8247249808 489.1314811843 628.2933247664 311.8281427313 285.9597028643 240.3162767362 155.403814758 2.2104492735 44.0369379065 503.5662623181 176.5432235636 466.3504706553 17.7478449293 error ^2 0 Mean Absolute Deviation 0 MAD = 298.3432032893 0 0 Mean Square Error 12340.75 MSE = 447.7802749251 1635.469 2522.676 2816.295 Estimate for 8269.297 Seasonal Factor 992.0114 Day 130.7249 Mon 1.3409478904 8449.234 Tue 1.1313714332 61162.98 Wed 0.9159417934 32206.37 Thur 0.8496057231 1270134 Fri 0.7621331599 1717963 115020.6 Describe your model here: 2397991 1414744 44053.95 25065.56 12218.19 111033.4 100630 221438.1 44032.04 7492.054 9454.114 11526.56 97942.86 47920.82 11135.83 7776.318 11813.71 151956.8 986169.6 444653.9 2160.828 11386.18 588069.1 153526.6 239249.6 394752.5 97236.79 81772.95 57751.91 24150.35 4.886086 1939.252 253579 31167.51 217482.8 314.986 790.3419724226 1357.1504890784 1138.6295335862 909.5121473676 742.7214566557 673.6090954116 1133.1125364069 960.0684309897 757.1796660171 684.3467905871 575.1364617505 32.3419724226 471.1504890784 260.6295335862 107.5121473676 202.2785433443 63.6090954116 223.1125364069 206.0684309897 52.1796660171 44.6532094129 196.8635382495 0 1046.003 221982.8 67927.75 11558.86 40916.61 4046.117 49779.2 42464.2 2722.718 1993.909 38755.25 0 Parts f and g Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 3 3 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 954 1,346 904 Seasonally Adjusted Call Volume 842.6874810549 752.1844506718 937.8325197479 974.5697062482 952.58944 809.1291300394 921.0061076381 973.8610100293 988.6939048895 1048.3732266667 971.700697181 990.8328662787 1095.0477500666 1310.0194239786 1318.6672 1977.7054865111 2496.9695336639 2009.9530487264 0 0 1453.4494695362 1332.0117122943 1079.7629360078 1165.2463879055 1422.3236266667 939.6338284329 1002.3233455486 1027.3578592349 996.9330207636 936.84416 747.2326159442 748.6489185888 1006.6141830123 991.0479379964 1028.6916266667 613.7449530161 0 0 471.9836379294 562.89376 901.6010306153 733.6229072358 0 1273.5319108219 1103.4817066667 1015.6994240679 1037.6786663793 1055.7439424869 1094.6253946991 1119.2269866667 689.0648075174 843.2244018107 1469.5256945061 1064.0229643096 OPTIMAL Expo Seasonally Adjusted Forecast Your Model 842.6874810549 819.987937505 849.5451602347 880.9032276389 898.8832255741 876.3715263332 887.5665616583 909.2105285025 929.1461743715 959.0501417242 962.2230944232 969.3988625653 1000.913524359 1078.4420093196 1138.6941594913 1349.1310263666 1637.0264711308 1730.5621577615 1296.5107133002 971.3260065021 1092.2499413056 1152.3858587343 1134.1709195198 1141.9651220451 1212.2833208756 1143.8986601481 1108.3894069691 1088.0654560591 1065.2080481354 1033.0124226781 961.3344784018 907.9896886531 932.7262195219 947.3541980858 967.7548685882 878.963769974 658.5062196483 493.3427931033 487.9855904659 506.7737045145 605.8024336695 637.8617624456 477.8762813611 677.4388765053 784.2969312736 842.3362139418 891.3310872348 932.5683447295 973.2147302459 1009.8368362617 929.3823077752 907.7725878539 1048.668854584 3 4 4 4 4 4 5 5 5 5 5 Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 758 886 878 802 945 610 910 754 705 729 772 994.5768533333 660.7266444377 776.0492922325 875.6014910801 1112.2806430007 800.3850666667 678.624431646 666.4477976575 769.6995651016 858.0450674577 1012.9463466667 1052.5199000232 1037.9868981316 943.364259286 901.3991077866 894.9286711456 949.4438683705 912.0576422248 853.5090244924 806.5912091766 797.3382208759 812.5644260309 862.8232749869 Final Forecast w/ Seasonal Factor 0 1130 927.7109280755 778.1339175973 748.4204237098 685.068713093 1175.1685494567 1004.1674529386 832.7839220094 789.4079073536 730.9239150203 1290.2910285758 1096.7501804993 916.7785284898 916.2505031623 867.8365779393 1809.1144037003 1852.0849848571 1585.094206284 1101.5229220958 740.279758634 1464.6502546002 1303.776440615 1038.8345459906 970.2201032837 923.9213180399 1533.9084951746 1254.0001119249 996.6046251051 905.0068540007 787.2930219175 1289.0994407965 1027.2735953975 854.3229262136 804.8775485079 737.5580760112 1178.6446130982 745.0151255057 451.8732826514 414.595350456 386.2290447788 812.3494954377 721.6585763723 437.7068581494 575.5559465374 597.7386985359 1129.5289691058 1008.4265296355 854.1783220931 826.8488046337 769.6301390093 1246.2532450006 1027.0279737552 960.5196312981 Forecasting Error 279 68.7109280755 49.8660824027 22.4204237098 399.931286907 133.1685494567 112.1674529386 7.2160779906 9.5920926464 572.0760849797 169.2910285758 93.7501804993 196.2214715102 88.7494968377 1784.163422061 1015.8855963 11.0849848571 1585.094206284 1101.522922096 1208.720241366 42.3497453998 314.776440615 48.8345459906 113.7798967163 336.0786819601 399.9084951745 313.0001119249 149.6046251051 191.0068540007 214.7069780825 442.0994407965 105.2735953975 12.3229262136 20.8775485079 85.4419239888 1178.644613098 745.0151255057 50.8732826514 14.404649544 822.7709552212 17.6505045623 721.6585763723 644.2931418506 265.4440534626 764.2613014641 44.4710308942 41.4265296355 75.8216779069 26.1511953663 154.3698609907 292.2532450006 318.9720262448 56.5196312981 error ^2 77841 Mean Absolute Deviation 4721.192 MAD = 312.3050053327 2486.626 502.6754 Mean Square Error 159945 MSE = 497.8455844148 17733.86 12581.54 52.07178 Estimate for 92.00824 Seasonal Factor 327271 Day 28659.45 Mon 1.3409478904 8789.096 Tue 1.1313714332 38502.87 Wed 0.9159417934 7876.473 Thur 0.8496057231 3183239 Fri 0.7621331599 1032024 122.8769 Describe your model here: 2512524 1213353 1461005 1793.501 99084.21 2384.813 12945.86 112948.9 159926.8 97969.07 22381.54 36483.62 46099.09 195451.9 11082.53 151.8545 435.872 7300.322 1389203 555047.5 2588.091 207.4939 676952 311.5403 520791.1 415113.7 70460.55 584095.3 1977.673 1716.157 5748.927 683.885 23830.05 85411.96 101743.2 3194.469 894.2269307489 791.0842346138 1265.0023133829 1019.8172004769 819.7025719696 806.6529443411 695.1093728849 1144.5111258436 912.5542523462 730.3153999357 690.359386753 136.2269307489 94.9157653862 387.0023133829 217.8172004769 125.2974280304 196.6529443411 214.8906271151 390.5111258436 207.5542523462 1.3153999357 81.640613247 0 18557.78 9009.003 149770.8 47444.33 15699.45 38672.38 46177.98 152498.9 43078.77 1.730277 6665.19 0 Parts f and g Week 44 44 44 44 44 45 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52/1 52/1 52/1 52/1 52/1 2 2 2 2 2 3 3 3 3 Day Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur True Value 1,130 851 859 828 726 1,085 1,042 892 840 799 1,303 1,121 1,003 1,113 1,005 2,652 2,825 1,841 0 0 1,949 1,507 989 990 1,084 1,260 1,134 941 847 714 1,002 847 922 842 784 823 0 0 401 429 1,209 830 0 1,082 841 1,362 1,174 967 930 853 924 954 1,346 904 Seasonally Adjusted Call Volume 842.6874810549 752.1844506718 937.8325197479 974.5697062482 952.58944 809.1291300394 921.0061076381 973.8610100293 988.6939048895 1048.3732266667 971.700697181 990.8328662787 1095.0477500666 1310.0194239786 1318.6672 1977.7054865111 2496.9695336639 2009.9530487264 0 0 1453.4494695362 1332.0117122943 1079.7629360078 1165.2463879055 1422.3236266667 939.6338284329 1002.3233455486 1027.3578592349 996.9330207636 936.84416 747.2326159442 748.6489185888 1006.6141830123 991.0479379964 1028.6916266667 613.7449530161 0 0 471.9836379294 562.89376 901.6010306153 733.6229072358 0 1273.5319108219 1103.4817066667 1015.6994240679 1037.6786663793 1055.7439424869 1094.6253946991 1119.2269866667 689.0648075174 843.2244018107 1469.5256945061 1064.0229643096 Optimal HOLT Seasonally Adjusted Forecast Your Model 845.3068482181 824.2248222627 855.7594747961 888.6182695984 907.5194969575 885.096674198 896.8556642775 919.0743332199 939.4131844211 969.7649217073 972.8769799599 980.0664562661 1011.9507147709 1090.4341472875 1151.1430981337 1364.1380636519 1655.0842427899 1748.0243630339 1305.7388125729 976.0232128263 1100.156498162 1161.7873568844 1143.5299737088 1151.6765747445 1223.1806822393 1153.6320680499 1117.740533338 1097.3558182774 1074.4157038909 1042.0205382498 969.6108617318 915.9912786887 941.6758711633 956.8613534173 977.7628695475 887.7328637426 664.4076016616 497.9227986901 493.9401639445 514.109511887 615.3527231257 648.0740657715 485.7464533938 688.8719642096 797.0172709507 855.2953390886 904.3346766597 945.4905358565 986.0675159063 1022.5784606827 940.3123608434 918.2210252675 1061.1577493512 3 4 4 4 4 4 5 5 5 5 5 Fri Mon Tue Wed Thur Fri Mon Tue Wed Thur Fri 758 886 878 802 945 610 910 754 705 729 772 994.5768533333 660.7266444377 776.0492922325 875.6014910801 1112.2806430007 800.3850666667 678.624431646 666.4477976575 769.6995651016 858.0450674577 1012.9463466667 1064.5063673487 1049.327364346 953.0405749729 910.6123479876 904.3207967805 959.869837127 921.8973451809 862.5992025855 815.2943658894 806.3090028683 822.0961667975 873.2904768213 Final Forecast w/ Seasonal Factor 0 1133.5124348718 932.5044184562 783.8258680211 754.9751675126 691.6507018922 1186.8685180795 1014.6768782823 841.8185929915 798.130817851 739.0900041465 1304.577333911 1108.8191912735 926.8879524692 926.4390922121 877.3243268842 1829.2380586894 1872.5150318598 1601.088569897 1109.3631680513 743.8596553326 1475.2525353372 1314.4130270514 1047.4068948685 978.4710090769 932.2265584906 1546.9604879671 1264.5797091671 1005.1140561362 912.8297310271 794.158405503 1300.1976395632 1036.3263657842 862.5202861878 812.9548820879 745.1855054067 1190.4035108881 751.691780532 456.0683011821 419.6543901621 391.819906832 825.1559359368 733.2124846225 444.915477635 585.2695632838 607.4332912091 1146.906480633 1023.1384192402 866.014297008 837.7686048887 779.3409534916 1260.9098766045 1038.8490373667 971.9587319681 Forecasting Error 282.5124348718 73.5044184562 44.1741319789 28.9751675126 393.3492981078 144.8685180795 122.6768782823 1.8185929915 0.869182149 563.9099958535 183.577333911 105.8191912735 186.1120475308 78.5609077879 1774.675673116 995.7619413106 31.5150318598 1601.088569897 1109.363168051 1205.140344667 31.7474646629 325.4130270514 57.4068948685 105.5289909231 327.7734415094 412.9604879671 323.5797091671 158.1140561362 198.8297310271 207.841594497 453.1976395631 114.3263657842 20.5202861878 28.9548820879 77.8144945933 1190.403510888 751.691780532 55.0683011821 9.3456098379 817.180093168 4.8440640632 733.2124846225 637.084522365 255.7304367162 754.5667087909 27.093519367 56.1384192402 63.985702992 15.2313951113 144.6590465084 306.9098766045 307.1509626333 67.9587319681 error ^2 79813.28 Mean Absolute Deviation 5402.9 MAD = 313.5033145001 1951.354 839.5603 Mean Square Error 154723.7 MSE = 498.6990148137 20986.89 15049.62 3.30728 Estimate for 0.755478 Seasonal Factor 317994.5 Day 33700.64 Mon 1.3409478904 11197.7 Tue 1.1313714332 34637.69 Wed 0.9159417934 6171.816 Thur 0.8496057231 3149474 Fri 0.7621331599 991541.8 993.1972 Describe your model here: 2563485 1230687 1452363 1007.902 105893.6 3295.552 11136.37 107435.4 170536.4 104703.8 25000.05 39533.26 43198.13 205388.1 13070.52 421.0821 838.3852 6055.096 1417061 565040.5 3032.518 87.34042 667783.3 23.46496 537600.5 405876.7 65398.06 569370.9 734.0588 3151.522 4094.17 231.9954 20926.24 94193.67 94341.71 4618.389 904.4107019886 799.7271799645 1277.9777484902 1030.2407972476 828.3052123669 815.5109070656 702.6085367914 1156.7005809811 922.4007552298 738.5321140816 698.4576082596 146.4107019886 86.2728200355 399.9777484902 228.2407972476 116.6947876331 205.5109070656 207.3914632086 402.7005809811 217.4007552298 9.5321140816 73.5423917404 0 21436.09 7442.999 159982.2 52093.86 13617.67 42234.73 43011.22 162167.8 47263.09 90.8612 5408.483 0 Question 1 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Forecasts MA(3) = MA(5) = MAE MA(3) MA(5) Part Grader b c Orders MA(3) MA(5) Delivered Forecast Forecast 120 90 100 75 103 110 88 50 95 99 75 78 85 130 78 82 110 85 88 90 105 95 Value 110 91 Part d e Grader Value 27.14 26.80 Part h i Grader f g MA(3) Error MA(5) Error Part Grader Is the time pattern stationary? (Yes or No) Delivery Orders - Past 28 22 45 3 52 25 15 49 10 48 22 5 140 120 100 80 Number of Orders 60 40 20 0 Jan Feb Mar Apr StatTools MA(3) MA(5) Confirm Best? Best? MA(5) Part j a Grader No me pattern stationary? (Yes or No) No Delivery Orders - Past 10 Months 140 120 100 80 er of Orders 60 40 20 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Month Part k.1. k.2. k.3. Grader Part l Grader Moving Averages Forecasts for Orders Delivered MA(3) Forecasting Constant 3 Span Moving Averages 27.14 31.23 33.01% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 StatTools Student Version F or Academic Use Only 60.00 Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 StatTools Student Version F or Academic Use Only 0.00 -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 Forecast Error 103.33 88.33 95.00 78.33 78.33 85.00 105.00 110.00 -28.33 21.67 -45.00 -3.33 51.67 25.00 -15.00 Moving Averages Forecasts for Orders Delivered MA(5) Forecasting Constant 5 Span Moving Averages 26.80 32.60 34.76% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 tions sion Orders Delivered Forecast sion 08 May-2008 Jun-2008 Forecast Error 99.00 85.00 82.00 88.00 95.00 91.00 -49.00 -10.00 48.00 22.00 -5.00 alpha = 0.20 Question 2 Part Grader Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct a c Orders ES Delivered Forecast ES Error 120 90 120 30 100 114 14 75 111 36.2 110 104 6.04 50 105 55 75 94 19 130 90 40 110 98 12 90 101 11 Nov Forecast = Value 98 Part b Grader Part d Grader MAPE Value 24.7% Part e.1. e.2. Grader Part f Grader StatTools ES(alpha=0.2) Optimal ES Metric alpha MAPE Simple 0.2916224 30.88% Simple Exponential Smoothing Forecasts for Orders Delivered Forecasting Constant 0.200 Level (Alpha) Simple Exponential 24.73 29.21 32.21% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Forecasting Data Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered Level 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 120.00 114.00 111.20 103.96 105.17 94.13 90.31 98.25 100.60 98.48 Forecast 120.00 114.00 111.20 103.96 105.17 94.13 90.31 98.25 100.60 98.48 Simple Exponential Smoothing Forecasts for Orders Delivered Forecasting Constant (Optimized) 0.292 Level (Alpha) Simple Exponential 24.43 28.93 30.88% Mean Abs Err Root Mean Sq Err Mean Abs Per% Err Forecast and Original Observations 140.00 120.00 100.00 80.00 60.00 StatTools Student Version F or Academic Use Only Orders Delivered Forecast 40.00 20.00 0.00 Forecast Errors 60.00 40.00 20.00 0.00 StatTools Student Version F or Academic Use Only -20.00 -40.00 -60.00 Jan-2008 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Error Forecasting Data Jan-2008 -30.00 -14.00 -36.20 6.04 -55.17 -19.13 39.69 11.75 -10.60 Feb-2008 Mar-2008 Apr-2008 May-2008 Jun-2008 Jul-2008 Aug-2008 Sep-2008 Oct-2008 Nov-2008 Orders Delivered 120.00 90.00 100.00 75.00 110.00 50.00 75.00 130.00 110.00 90.00 tions ion Orders Delivered Forecast ion ul-2008 Aug-2008 Sep-2008 Oct-2008 Level 120.00 111.25 107.97 98.36 101.75 86.66 83.26 96.89 100.71 97.59 Forecast Error 120.00 111.25 107.97 98.36 101.75 86.66 83.26 96.89 100.71 97.59 -30.00 -11.25 -32.97 11.64 -51.75 -11.66 46.74 13.11 -10.71 Question 3 Time 1 2 3 4 5 6 7 8 9 10 11 12 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec StatTools ES (Simple) ES