BA6933 Week-7 (17,18)

 

Consider the following gasoline sales time series data. Click on the datafile logo to reference the data. Week Sales (1000s of gallons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 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)2                                                                                                                         Totals       b. Compute the MSE for the four-week and five-week moving average forecasts (to 2 decimals). MSE (-Week)   MSE (-Week)   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 . The  - Select your answer - 3-week 4-week 5-week Item 47   moving average provides the smallest MSE.

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Consider the following gasoline time series data. Click on the webfile logo to reference the data. Week Sales (1000s of gallons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 Show the exponential smoothing forecasts using  and  a. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of  or  for the gasoline sales time series? Calculate the MSE for each smoothing constant (to 2 decimals). MSE for    MSE for    - Select your answer - α = 0.1 α = 0.2 Item 3   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    MAE for    - Select your answer - α = 0.1 α = 0.2 Item 6   would be preferred based upon MAE. c. What are the results if MAPE is used (to 2 decimals)? MAPE for     MAPE for     - Select your answer - α = 0.1 α = 0.2 Item 9   would be preferred based upon MAPE.

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For the Hawkins Company, the monthly percentages of all shipments received on time over the past  months are , , , , , , , , , , , and . a. Construct a time series plot. - Select your answer - time series plot 1 time series plot 2 time series plot 3 Item 1   What type of pattern exists in the data? - Select your answer - parallel perpendicular vertical horizontal Item 2   b. Compare the three-month moving average approach with the exponential smoothing approach for  (to 2 decimals). Round intermediate calculations to 2 decimal places. MSE (-Month)   MSE ()   Which provides more accurate forecasts using MSE as the measure of forecast accuracy? - Select your answer - A 3-month moving average The exponential smoothing approach for α = 0.2 Item 5   provides the most accurate forecast using MSE. c. What is the forecast for next month (to 1 decimal)?

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Ten weeks of data on the Commodity Futures Index are , , , , , , , , , and . a. Construct a time series plot. A. B. C. - Select your answer - time series plot A time series plot B time series plot C Item 1   What type of pattern exists in the data? - Select your answer - parallel perpendicular vertical horizontal Item 2   b. Compute the exponential smoothing forecasts for . Round your Time-series values and Forecast values to two decimal places and (Error)2 values to four decimal places. Week Time-Series Value  Forecast (Error)2                                                             Total   c. Compute the exponential smoothing forecasts for . Round your Time-series values and Forecast values to two decimal places and (Error)2 values to four decimal places. Week Time-Series Value  Forecast (Error)2                                                             Total   d. Which exponential smoothing constant provides more accurate forecasts based on MSE (to 4 decimals)? MSE ()   MSE ()   Forecast week 11 (to 2 decimals).

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Consider the following time series. 1 2 3 4 5 6 7 120 110 100 96 94 92 88 Excel File: data17-19.xls a. Construct a time series plot. 1. 2. 3. - Select your answer - time series plot #1 time series plot #2 time series plot #3 Item 1   What type of pattern exists in the data? - Select your answer - linear trend curvilinear trend horizontal Item 2   b. Develop the linear trend equation for this time series (to 1 decimal).        c. What is the forecast for  (to 1 decimal)?

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The following data show the number of Netflix subscribers worldwide for the years  (period ) to  (period ) (datawrapper website). The data are in the file NetflixSubscribers. Click on the datafile logo to reference the data. 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. A. B. C. - Select your answer - Graph A Graph B Graph C Item 1   What type of pattern exists in the data? - Select your answer - Downward Upward Item 2   b. Develop a linear trend equation for this time series (to  decimals).     +   c. Develop a quadratic trend equation for this time series (to  decimals).     +    +   d. Compare the MSE for each model (to  decimals). Linear model   Quadratic model     Which model appears better according to MSE? - Select your answer - Quadratic model Linear model Item 10   e. Use the models developed in parts (b) and (c) to forecast subscribers for  (to  decimal). Linear model $    million Quadratic model $    million   f. Which of the two forecasts in part (e) would you use? Explain. For the forecast one period ahead, the  - Select your answer - quadratic linear Item 13   model is likely slightly preferred because of its  - Select your answer - lower higher Item 14   MSE.

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Consider the following time series. Quarter Year 1 Year 2 Year 3 1 71 68 62 2 49 41 51 3 58 60 53 4 82 81 68 a. Construct a time series plot. - Select your answer - Plot 1 Plot 2 Plot 3 Plot 4 Item 1   What type of pattern exists in the data? - Select your answer - Horizontal Vertical Item 2   b. Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data:  if Quarter ,  otherwise;  if Quarter ,  otherwise;  if Quarter ,  otherwise. Enter negative values as negative numbers.  =   +   Qtr1 +   Qtr2 +   Qtr3 c. Compute the quarterly forecasts for next year. Quarter  forecast   Quarter  forecast   Quarter  forecast   Quarter  forecast

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South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from  in the first year of operation to  in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 13 32 74 92 167 2 108 136 160 209 273 3 183 239 336 386 447 4 12 25 57 78 182 a. Construct a time series plot. 1. 2. 3. 4. - Select your answer - Time series plot 1 Time series plot 2 Time series plot 3 Time series plot 4 Item 1   What type of pattern exists in the data? There appears to be a seasonal pattern in the data and perhaps a  - Select your answer - upward linear trend downward linear trend horizontaly plot Item 2  . b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data:  if Quarter ,  otherwise;  if Quarter ,  otherwise;  if Quarter ,  otherwise. Round your answers (in thousands of dollars) to whole number.                Based only on the seasonal effects in the data, compute estimates of quarterly sales for year . Round your answers to whole number. Quarter  forecast $   thousands Quarter  forecast $   thousands Quarter  forecast $   thousands Quarter  forecast $   thousands c. Let  to refer to the observation in quarter  of year ;  to refer to the observation in quarter  of year ; . . . and  to refer to the observation in quarter  of year . Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Round your answers (in thousands of dollars) to whole number. Enter negative value as negative number. The regression equation is:                    Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales for year . Round your answers to whole number. Quarter  forecast $   thousands Quarter  forecast $   thousands Quarter  forecast $   thousands Quarter  forecast $   thousands

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The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. Do not round your intermediate calculations. Click on the datafile logo to reference the data. 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 4 2,500 2,360 2,615 a. Construct a time series plot. 1. 2. 3. - Select your answer - time series plot 1 time series plot 2 time series plot 3 Item 1   What type of pattern exists in the data? - Select your answer - upward linear trend nonlinear trend and a seasonal pattern linear trend and a seasonal pattern slight curvature downward linear trend Item 2   b. Show the four-quarter and centered moving average values for this time series (to 3 decimals if necessary). Year Quarter Time Series Value Four-Quarter Moving Average   Centered Moving Average                                                                                                                                                                                                       c. Compute the seasonal and adjusted seasonal indexes for the four quarters (to 3 decimals). Quarter Seasonal Index Adjusted Seasonal Index                 Total     d. When does the publisher have the largest seasonal index? The largest seasonal index is in the  - Select your answer - first second third fourth Item 29   quarter. Does this result appear reasonable? - Select your answer - Yes No Item 30   e. Deseasonalize the time series (to 3 decimals). Year Quarter Deseasonalized Value                                           f. Compute the linear trend equation for the deseasonalized data (to 1 decimal if necessary). Let  denote the time series value in ;  denote the time series value in ; and so on. =   +   Period Compute the forecast sales using the linear trend equation (to 1 decimal). Forecast for quarter    Forecast for quarter    Forecast for quarter    Forecast for quarter    g. Adjust the linear trend forecasts using the adjusted seasonal indexes computed in part (c) (to the nearest whole number). Forecast for quarter    Forecast for quarter    Forecast for quarter    Forecast for quarter

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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  weeks follow. Click on the datafile logo to reference the data. 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? 1. 2. 3. - Select your answer - time series plot 1 time series plot 2 time series plot 3 Item 1   What type of pattern exists in the data? - Select your answer - nonlinear trend and a seasonal pattern slight upward linear trend and a seasonal pattern seasonal pattern and slight curvature horizontal Item 2   b. Use exponential smoothing with  to develop a forecast of demand for week  (to the nearest whole number).   half-gallons of milk

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Hudson Marine provides boats sales, service, and maintenance. Boat trailers are one of its top sales items. Suppose the quarterly sales values for the seven years of historical data are as follows. Do not round intermediate calculations. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 8 16 8 5 37 2 8 17 16 8 49 3 14 24 23 13 74 4 17 26 26 18 87 5 24 36 28 23 111 6 24 38 28 20 110 7 27 40 33 29 129 a. Compute the centered moving average values (first find Four-Quarter Moving Average) for this time series (to 3 decimals). t Sales Centered Moving Average                                                 b. Choose a time series plot that also shows the centered moving average and original time series on the same graph. Discuss the differences between the original time series plot and the centered moving average time series. - Select your answer - Time series plot 1 Time series plot 2 Time series plot 3 Time series plot 4 Item 25   The centered moving average values  - Select your answer - smooth out the time series by removing seasonal effects  smooth out the time series by removing some of the random values smooth out the time series by removing the trend line doesn't smooth Item 26  . c. Compute the seasonal indexes for the four quarters (to 3 decimals). Quarter Adjusted Seasonal Index         d. When does Hudson Marine experience the largest seasonal effect? Hudson Marine experiences the largest seasonal increase in quarter  . The largest seasonal effect is the seasonal decrease in quarter  . Does this result seem reasonable? This  - Select your answer - is also reasonable because of decreased boating in the fall and winter is also reasonable because of decreased boating in the summer and winter is also reasonable because of decreased boating in the summer and fall is not reasonable Item 33  .

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                           CHAPTER 18 ASST

 

 

    

The median number of part-time employees at fast-food restaurants in a particular city was known to be  last year. City officials think the use of part-time employees may be increasing. A sample of nine fast-food restaurants showed that seven restaurants were employing more than  part-time employees, one restaurant was employing exactly  part-time employees, and one restaurant was employing fewer than  part-time employees. Can it be concluded that the median number of part-time employees has increased? Test using . - Select your answer - Yes No Item 1

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Are stock splits beneficial to stockholders? SNL Financial studied stock splits in the banking industry over an -month period. For a sample of  stock splits,  led to an increase in investment value,  led to a decrease in investment value, and  resulted in no change. Conduct a sign test to determine if it can be concluded that stock splits are beneficial for holders of bank stocks. a.  What are the null and alternative hypotheses? Let  the probability the shares held will be worth more after the split. 1. :  :  2. :  :  3. :  :  4. :  :  Choose the correct option. - Select your answer - 1 2 3 4 Item 1   b.  Using , what is your conclusion? Conclusion:  - Select your answer - The results do not show that stock splits are beneficial to shareholders. The results show that stock splits are beneficial to shareholders. Item 2

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A test was conducted for two overnight mail delivery services. Two samples of identical deliveries were set up so that both delivery services were notified of the need for a delivery at the same time. The hours required to make each delivery follow. Do the data shown suggest a difference in the median delivery times for the two services? Use a  level of significance for the test. Use Table 1 of Appendix B. Click on the datafile logo to reference the data. Service Delivery 1 2 1 24.5 28.0 2 26.0 25.5 3 28.0 32.0 4 21.0 20.0 5 18.0 19.5 6 36.0 28.0 7 25.0 29.0 8 21.0 22.0 9 24.0 23.5 10 26.0 29.5 11 31.0 30.0 What is the -statistic (to  decimals)? Enter negative values as negative number, if necessary.   What is the -value (to  decimals)?   Conclude: - Select your answer - Reject the null hypothesis Do not reject the null hypothesis Item 3   Observe: There  - Select your answer - is is not Item 4   a significant difference.

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The Scholastic Aptitude Test (SAT) consists of three parts: evidence-based reading, mathematics, and writing. Each part of the test is scored on a - to -point scale with a median of approximately  (the College Board website). Scores for each part of the test can be assumed to be symmetric. Use the following data to test the hypothesis that the population median score for the students taking the writing portion of the SAT is . Using , what is your conclusion? Use Table 1 of Appendix B. Click on the datafile logo to reference the data. 635 701 439 447 464 502 405 453 471 476 447 590 337 387 514 Conclusion:  - Select your answer - We cannot reject the hypothesis that the population median score for the writing portion is 500. We can reject the hypothesis that the population median score for the writing portion is 500. Item 1

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Three admission test preparation programs are being evaluated. The scores obtained by a sample of  people who used the test preparation programs provided the following data. Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use . Use Table 3 of Appendix B. Click on the datafile logo to reference the data. Program A B C 540 450 600 400 540 630 490 400 580 530 410 490 490 480 590 610 370 620 550 570 Compute the value of the test statistic  (to  decimals):   What is the -value (to  decimals)?   Conclude: - Select your answer - Reject the null hypothesis Do not reject the null hypothesis Item 3   Observe: We  - Select your answer - can cannot Item 4   conclude that there is a significant difference in test preparation programs.

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The following data show the rankings of  states based on expenditure per student (ranked  highest to  lowest) and student-teacher ratio (ranked  lowest to  highest). Use Table 1 of Appendix B. State Expenditure per Student Student-Teacher Ratio Arizona 10 10 Colorado 5 8 Florida 4 7 Idaho 2 10 Iowa 7 5 Louisiana 10 4 Massachusetts 1 1 Nebraska 7 2 North Dakota 8 8 South Dakota 11 5 Washington 3 10 a. What is the rank correlation between expenditure per student and student-teacher ratio (to  decimals)? Enter negative values as negative numbers.    b. At the  level, does there appear to be a relationship between expenditure per student and student-teacher ratio? Enter negative values as negative numbers.    (to  decimals) -value    (to  decimals) Conclusion: - Select your answer - We can conclude that there is a significant relationship. We cannot conclude that there is a significant relationship. Item 4

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A national study by Harris Interactive, Inc., evaluated the top technology companies and their reputations. The following shows how  technology companies ranked in reputation and how the companies ranked in percentage of respondents who said they would purchase the company's stock. A positive rank correlation is anticipated because it seems reasonable to expect that a company with a higher reputation would have the more desirable stock to purchase. Use Table 1 of Appendix B. Click on the datafile logo to reference the data. Company Reputation Stock Purchase Microsoft 1 3 Intel 2 4 Dell 3 1 Lucent 4 2 Texas Instruments 5 9 Cisco Systems 6 5 Hewlett-Packard 7 10 IBM 8 6 Motorola 9 7 Yahoo 10 8 a. Compute the rank correlation between reputation and stock purchase (to  decimals).    b. Test for a significant positive rank correlation. What is the -statistic (to  decimals)?   What is the -value (to  decimals)?   c. At , what is your conclusion? - Select your answer - Reject the null hypothesis Do not reject the null hypothesis Item 4   Observe: There  - Select your answer -  is  is not Item 5   a positive rank correlation.

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