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Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

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Lesson06 Lesson06 Presentation Transcript

  • IBS Statistics
    Year 1
    Dr. Ning DING
    n.ding@pl.hanze.nl
    I.007
  • What we are going to learn?
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
  • Review
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Why Dispersion?
    Central Tendency?
  • Review
    Dispersion
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Range Variance Standard Deviation
  • Review
    Dispersion
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
  • Review
    Don’tcompare the dispersion in data sets byusingtheir Standard Deviationsunlesstheirmeans are close to eachother.
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Whichone has more variation in the data?
    Example :
    20 poundsoverweight
    Mean=120 pounds
    Mean=170 pounds
    CV=20/120 =16.7%
    CV=20/170 =12.5%
    Coefficient of Variation (CV)= Standard Deviation / Mean
  • Review
    2
    3
    4
    5
    6
    7
    10
    13
    2
    3
    4
    4.25
    4.75
    7
    8
    9
    2
    3
    4
    5
    6
    7
    8
    9
    2
    3
    3.25
    3.50
    3.75
    4
    5
    9
    Median= 5.5 5.5 4.5 3.38
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Mean= 5.5 6.25 5.25 4.19
  • Review
    Most skewed?
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Median= 5.5 5.5 4.5 3.38
    Mean= 5.5 6.25 5.25 4.19
  • Review
    Positive Correlation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Negative Correlation
  • Review
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Secular trend
    Seasonalvariation
    Sales
    Q4
    Q2
    Q3
    Cyclicalfluctuation
    Q1
    Irregularvariation
    2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
    Years
  • Review
    Applicable when time series follows fairly linear trendthat have definite rhythmic pattern
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
  • Seven-Year Moving Total
    Moving Average
    1+2+3+4+5+4+3=22
    / 7 = 3.143
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    2+3+4+5+4+3+2=23
    / 7 = 3.286
    3+4+5+4+3+2+3=24
    / 7 = 3.429
    SevenYearMoving Average
  • Ŷ = a + bt
    Review
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    = 1.73
    a = 22.67 -1.73*4 = 15.75
    a = Y - bX
    P152 N6 Ch16
  • Ŷ = a + bt
    Review
    = 1.73
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    a = 22.67 = 22.67
    a = Y - bX
    a = Y
    Ŷ = 22.67 + 1.73t
  • Ŷ = a + bt
    Review
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    a = Y
    Odd-numbered
    Even-numbered
  • Seasonal Variation
    Understanding seasonal fluctuationshelp plan for sufficient goods and materials on hand to meet varying seasonal demand
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
  • Seasonal Variation
    Seasonal variations are fluctuations that coincide with certain seasons and are repeated year after year
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
  • Seasonal Variation
    Seasonal Index:
    A number, usually expressed in percent, that expresses the relative valueof a season with respect to the average for the year(100%)
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    SalesforJuly are 14% belowan average month.
    Sales for December are 26.8% above an average month.
  • Seasonal Variation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Sales Report: in $ millions
    2005
    2006
    2007
    2008
    2009
    2010
  • Seasonal Variation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Step 1: Re-organize the data
    2005
    2006
    2007
    2008
    2009
    2010
  • Seasonal Variation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    6.7+4.6+10.0+12.7=34
    /4=8.50
    4.6+10.0+12.7+6.5=33.8
    /4=8.45
    Step 2: Moving Average
  • Seasonal Variation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Step 3: Centered Moving Average
  • Seasonal Variation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Step 4: SpecificSeasonal Index
  • Seasonal Variation
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    10/8.475=1.180
    12.7/8.45=1.503
    6.5/8.425=0.772
    Step 4: Specific Seasonal Index
  • Seasonal Variation
    2005
    2006
    2007
    2008
    2009
    2010
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    + + + =
    *(0.9978)
    *(0.9978)
    *(0.9978)
    *(0.9978)
    Step 5: TypicalQuarterly Index
  • Seasonal Variation
    Sales for the Winter are 23.5% below the typical quarter.
    2005
    2006
    2007
    2008
    2009
    2010
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Salesfor the Fall are 51.9% above the typicalquarter.
    Step 6: Interpret
  • Exercise
    Appliance Center sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in $ millions) were reported.
    Determine a typical seasonal index for each of the four quarters.
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    P161 No.10 Ch16
  • Exercise
    Step 1: Reorganize the data
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Step 2: Moving Average
    Step 3: Centered Moving Average
    Step 4: Specific Seasonal Index
    P161 No.10 Ch16
  • Step 5: Reorganize the data
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Step 6: Calculate the mean for each quarter
    Step 8: Divide 4 by Total of four means to get Correction Factor
    Step 7: Sum up the four means
    Step 9: Mean * Correction Factor
    P161 No.10 Ch16
  • DeseasonalizingData
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to develop seasonally adjusted forecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    To remove the seasonal fluctuations so that the trend and cycle can be studied.
    Ŷ = a + bt
    Ŷ = a + bX
  • 76.5
    57.5
    114.1
    151.9
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    / 0.765
    = 8.759
    / 0.575
    = 8.004
    / 1.141
    = 8.761
    / 1.519
    = 8.361
    / 0.765
    / 0.575
    / 1.141
    / 1.519
    / 0.765
    / 0.575
    / 1.141
    = 8.498
    = 9.021
    / 1.519
    = 8.004
    = 8.700
    = 8.586
    = 9.112
    = 8.953
    = 9.283
  • DeseasonalizingData
    Ŷ = a + bt
    Chapter 16: Time Series & Forecasting
    76.5
    57.5
    114.1
    151.9
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    Ŷ = 8.1096 + 0.0899 t
    Sale increased at a rate of 0.0899 ($ millions) per quarter.
    Ŷ = 8.1096 + 0.0899 * 25
    = 10.3571 $ millions
    10.3571*0.765 = 7.9232 $ millions
  • Home Assignment
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to develop seasonally adjusted forecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
    1. Calculate the seasonal indices for each quarter, express them as a ratio and not as a %. You may round to 4 dec. places.
    Wed, 06, 12:00 a.m. 2011
    Pigeon hole Ning Ding
    2. Interpret the seasonal index quarter II.
    3. Deseasonalized the original revenue for 2008 quarter I.
    4. For 2011 quarter II the forecasted revenue from the trend line was 55. Calculate the seasonalized revenue for 2011 quarter II.
  • What we have learnt?
    • Review
    • Chapter 16:
    • Use a trend equation to forecast future time periods
    • Use a trend equation to developseasonallyadjustedforecasts
    • Determine and interpret a set of seasonal indexes
    • Desearsonalize data using a seasonal index
  • Step 7: Sum up the four means
    Step 1: Reorganize the data
    Step 8: Divide 4 by Total of four means to get Correction Factor
    Step 2: Moving Average
    Step 3: Centered Moving Average
    Step 9: Mean * Correction Factor
    Step 4: Specific Seasonal Index
    Step 5: Reorganize the data
    Step 6: Calculate the mean for each quarter
    Hint