Lesson 6

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Introductory Business Statistics
Hanze University of Applied Sciences

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Lesson 6

  1. 1. Hanze University of Applied Science GroningenNing Ding, PhDLecturer of International BusinessSchool (IBS)n.ding@pl.hanze.nl
  2. 2. What we are going to learn?• 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
  3. 3. Review•Review Central Tendency? Why Dispersion?•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  4. 4. Review Dispersion•Review Range Variance Standard Deviation•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  5. 5. Review Dispersion•Review•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  6. 6. Review Don’t compare the dispersion in data sets by using their Standard•Review Deviations unless their means are close to each other.•Chapter 16: Which one has more variation in the data?–Use a trendequation to A Bforecast futuretime periods–Use a trendequation to Example :develop 20 pounds overweightseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using a Mean=120 pounds Mean=170 poundsseasonal index CV=20/120 =16.7% CV=20/170 =12.5% Coefficient of Variation (CV)= Standard Deviation / Mean
  7. 7. Review Salary in hundreds of dollars•Review•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalize Companiesdata using aseasonal indexCompany 1: 350 25% of the employees earned money less than _______dollars. Company 2: Comment on the skewness. Positive skewness Company 3: The range of salary is ________dollars. 700 Company 4: Which one has the widest range? Company 2
  8. 8. Review•Review Positive Correlation Negative Correlation•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  9. 9. Review•Review•Chapter 16: Secular trend Seasonal variation–Use a trend Salesequation toforecast futuretime periods–Use a trend Q4equation to Q2developseasonallyadjusted forecasts–Determine andinterpret a set of Q3 Cyclical fluctuationseasonal indexes Q1–Desearsonalizedata using a Irregular variationseasonal index 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Years
  10. 10. Review•Review Applicable when time series follows fairly linear trend that have definite rhythmic pattern•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  11. 11. Review Seven-Year Moving Total Moving Average 1+2+3+4+5+4+3=22 / 7 = 3.143•Review•Review 2+3+4+5+4+3+2=23 / 7 = 3.286 3+4+5+4+3+2+3=24 / 7 = 3.429 Seven Year Moving Average•Chapter 16:•Chapter 16:–Use a trend–Use a trendequation toequation toforecast futuretime periodsforecast future–Use a trendtime periodsequation to–Use a trenddevelopseasonally toequationadjusted forecastsdevelop and–Determineseasonallyinterpret a set ofadjusted forecastsseasonal indexes–Desearsonalize–Determine anddata using ainterpret aseasonal index set ofseasonal indexes–Desearsonalizedata using aseasonal index
  12. 12. Review•Review Ŷ = a + bt xy a Y b= 2•Chapter 16: x–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  13. 13. Seasonal Variation•Review Understanding seasonal fluctuations help plan for sufficient goods and materials on hand to meet varying•Chapter 16:–Use a trend seasonal demandequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  14. 14. Seasonal Variation•Review Seasonal variations are fluctuations that coincide with certain seasons and are repeated year after year•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index
  15. 15. Seasonal Variation•Review Seasonal Index: A number, usually expressed in percent, that expresses•Chapter 16:–Use a trend the relative value of a season with respect to the averageequation toforecast future for the year (100%)time periods–Use a trend Sales for the Winter are 23.5% below the typical quarter.equation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index Sales for the Fall are 51.9% above the typical quarter.
  16. 16. Seasonal Variation•Review•Chapter 16: Sales Report: in $ millions–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine and 2005interpret a set ofseasonal indexes 2006–Desearsonalize 2007 2008data using aseasonal index 2009 2010
  17. 17. Seasonal Variation Step 1: Re-organize the data•Review•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonally 2005adjusted forecasts–Determine and 2006interpret a set ofseasonal indexes–Desearsonalizedata using a 2007seasonal index 2008 2009 2010
  18. 18. Seasonal Variation Seasonal Variation•Review 6.7+4.6+10.0+12.7=34 /4=8.50•Review 4.6+10.0+12.7+6.5=33.8 /4=8.45•Chapter 16:•Chapter 16:–Use a trend–Use a trendequation toequation toforecast futureforecast futuretime periods–Use aperiodstime trendequation to–Use a trenddevelopseasonally toequationadjusted forecastsdevelop–Determine andseasonally ofinterpret a setadjusted forecastsseasonal indexes–Desearsonalize–Determinedata using aand interpret aseasonal indexset of seasonalindexes–Desearsonalizedata using aseasonal index Step 2: Moving Average
  19. 19. Seasonal Variation Seasonal Variation•Review•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index Step 3: Centered Moving Average
  20. 20. Seasonal Variation Seasonal Variation•Review•Chapter 16:–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index Step 4: Specific Seasonal Index
  21. 21. Seasonal Variation•Review•Review 10/8.475=1.180 12.7/8.45=1.503•Chapter 16:•Chapter 16: 6.5/8.425=0.772–Use a trend–Use a trendequation toequation toforecast futureforecast futuretime periods–Use aperiodstime trendequation to–Use a trenddevelopseasonally toequationadjusted forecastsdevelop–Determine andseasonally ofinterpret a setadjusted forecastsseasonal indexes–Desearsonalize–Determinedata using aand interpret aseasonal indexset of seasonalindexes–Desearsonalizedata using aseasonal index Step 4: Specific Seasonal Index
  22. 22. Seasonal Variation Seasonal Variation 2005 2006•Review 2007 2008•Chapter 16:–Use a trend 2009equation toforecast future 2010time periods–Use a trendequation todevelopseasonallyadjusted forecasts *(0.9978) + *(0.9978) + *(0.9978) + *(0.9978) =–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index Step 5: Typical Quarterly Index
  23. 23. Seasonal Variation Sales for the Winter are 23.5% below the typical quarter.•Review 2005•Chapter 16:–Use a trend 2006equation toforecast future 2007time periods–Use a trend 2008equation todevelop 2009seasonallyadjusted forecasts Sales for the Fall are 51.9% above the typical quarter. 2010–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index Step 6: Interpret
  24. 24. Exercise Appliance Center sells a variety of electronic equipment and home•Review appliances. For the last four years the following quarterly sales (in $•Chapter 16: millions) were reported.–Use a trendequation toforecast futuretime periods–Use a trendequation todevelopseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using a Determine a typical seasonal index for each of the four quarters.seasonal index In Quarter 3 the sales will be ________ than average quarter. A 12.60% higher 10.20% higher B C 21.00% higher D 17.60% higher P161 No.10 Ch16
  25. 25. Exercise A 12.60% higher 10.20% higher B C 21.00% higher D 17.60% higherStep 1: Reorganize the data Step 7: Sum up the four meansStep 2: Moving Average Step 8: Divide 4 by Total of four means to get Correction FactorStep 3: Centered Moving Average Step 9: Mean * Correction FactorStep 4: Specific Seasonal IndexStep 5: Reorganize the data HintStep 6: Calculate the mean for each quarter
  26. 26. P161 No.10 Ch16
  27. 27. P161 No.10 Ch16
  28. 28. Deseasonalizing Data•Review To remove the seasonal fluctuations so that the trend and•Chapter 16:–Use a trend cycle can be studied.equation toforecast futuretime periods–Use a trendequation todevelop Ŷ = a + bX Ŷ = a + btseasonallyadjusted forecasts–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index P161 No.10 Ch16
  29. 29. 76.5 Deseasonalizing Data 57.5 114.1 151.9•Review•Review / 0.765 = 8.759•Chapter 16:•Chapter 16: / 0.575 = 8.004–Use a trend–Use a trendequation to / 1.141 = 8.761equation to / 1.519 = 8.361forecast futureforecast futuretime periods / 0.765 = 8.498–Use aperiods / 0.575 = 8.004time trendequation to / 1.141 = 8.586–Use a trenddevelop / 1.519 = 8.953seasonally = 9.021equation toadjusted forecasts / 0.765 / 0.575 = 8.700develop and–Determine / 1.141 = 9.112interpret a set ofseasonally / 1.519 = 9.283seasonal indexesadjusted–Desearsonalizeforecastsdata using aseasonal index–Determine andinterpret a set ofseasonal indexes–Desearsonalizedata using aseasonal index P161 No.10 Ch16
  30. 30. Chapter 16: Time Series & Forecasting Ŷ = a + bt 76.5 Deseasonalizing Data 57.5 114.1 151.9•Review•Chapter 16: Ŷ = 9.2333 + 0.0449 t–Use a trendequation toforecast futuretime periods–Use a trend Sale increased at a rate ofequation todevelop 0.0449 ($ millions) per quarter.seasonallyadjusted forecasts–Determine and Ŷ = 9.2333+ 0.0449 * 25interpret a set ofseasonal indexes = 10.3558 $ millions–Desearsonalizedata using aseasonal index 10.3558*0.765 = 7.9222 $ millions xy b= 2 a Y x
  31. 31. Home Assignment•Review 1. Calculate the seasonal indices for each quarter, express them as a ratio and not as a•Chapter 16: %. You may round to 4 dec. places.–Use a trendequation toforecast future 2. Interpret the seasonal index quartertime periods II.–Use a trendequation to 3. Deseasonalized the original revenuedevelopseasonally for 2008 quarter I.adjusted forecasts–Determine andinterpret a set of 4. For 2011 quarter II the forecastedseasonal indexes revenue from the trend line was 55.–Desearsonalizedata using a Calculate the seasonalized revenue forseasonal index 2011 quarter II.
  32. 32. What we have learnt?•Review •Review•Chapter 16:–Use a trendequation to •Chapter 16:forecast futuretime periods–Use a trend – Use a trend equation to forecast future timeequation todevelop periodsseasonallyadjusted forecasts – Use a trend equation to develop seasonally–Determine andinterpret a set of adjusted forecastsseasonal indexes–Desearsonalize – Determine and interpret a set of seasonaldata using aseasonal index indexes – Desearsonalize data using a seasonal index

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