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Introductory Business Statistics

Hanze University of Applied Sciences

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- 1. Hanze University of Applied Science GroningenNing Ding, PhDLecturer of International BusinessSchool (IBS)n.ding@pl.hanze.nl
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. P161 No.10 Ch16
- 27. P161 No.10 Ch16
- 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. 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. 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. 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. 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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